Auxiliary Polynomials In Number Theory

Author by : David William Masser
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 37
Total Download : 907
File Size : 52,8 Mb
GET BOOK

Description : A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.


Auxiliary Polynomials In Number Theory

Author by : David Masser
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 45
Total Download : 430
File Size : 55,8 Mb
GET BOOK

Description : A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.


Number Theory And Polynomials

Author by : Chris Smyth
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 74
Total Download : 738
File Size : 46,6 Mb
GET BOOK

Description : Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.


Analytic Number Theory

Author by : Japan) Taniguchi International Symposium on Mathematics: Analytic Number Theory (1996 : Kyoto
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 38
Total Download : 851
File Size : 46,8 Mb
GET BOOK

Description : Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.


Advances In Cryptology Asiacrypt 2016

Author by : Jung Hee Cheon
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 63
Total Download : 965
File Size : 42,6 Mb
GET BOOK

Description : The two-volume set LNCS 10031 and LNCS 10032 constitutes the refereed proceedings of the 22nd International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2016, held in Hanoi, Vietnam, in December 2016. The 67 revised full papers and 2 invited talks presented were carefully selected from 240 submissions. They are organized in topical sections on Mathematical Analysis; AES and White-Box; Hash Function; Randomness; Authenticated Encryption; Block Cipher; SCA and Leakage Resilience; Zero Knowledge; Post Quantum Cryptography; Provable Security; Digital Signature; Functional and Homomorphic Cryptography; ABE and IBE; Foundation; Cryptographic Protocol; Multi-Party Computation.


Analytic Number Theory And Diophantine Problems

Author by : A.C. Adolphson
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 95
Total Download : 584
File Size : 47,5 Mb
GET BOOK

Description : A conference on Analytic Number Theory and Diophantine Problems was held from June 24 to July 3, 1984 at the Oklahoma State University in Stillwater. The conference was funded by the National Science Foundation, the College of Arts and Sciences and the Department of Mathematics at Oklahoma State University. The papers in this volume represent only a portion of the many talks given at the conference. The principal speakers were Professors E. Bombieri, P. X. Gallagher, D. Goldfeld, S. Graham, R. Greenberg, H. Halberstam, C. Hooley, H. Iwaniec, D. J. Lewis, D. W. Masser, H. L. Montgomery, A. Selberg, and R. C. Vaughan. Of these, Professors Bombieri, Goldfeld, Masser, and Vaughan gave three lectures each, while Professor Hooley gave two. Special sessions were also held and most participants gave talks of at least twenty minutes each. Prof. P. Sarnak was unable to attend but a paper based on his intended talk is included in this volume. We take this opportunity to thank all participants for their (enthusiastic) support for the conference. Judging from the response, it was deemed a success. As for this volume, I take responsibility for any typographical errors that may occur in the final print. I also apologize for the delay (which was due to the many problems incurred while retyping all the papers). A. special thanks to Dollee Walker for retyping the papers and to Prof. W. H. Jaco for his support, encouragement and hard work in bringing the idea of the conference to fruition.


Computer Algebra In Scientific Computing

Author by : Matthew England
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 29
Total Download : 304
File Size : 51,5 Mb
GET BOOK

Description : This book constitutes the refereed proceedings of the 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019, held in Moscow, Russia, in August 2019. The 28 full papers presented together with 2 invited talks were carefully reviewed and selected from 44 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CASs in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.


Polynomial Methods In Combinatorics

Author by : Larry Guth
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 32
Total Download : 192
File Size : 49,9 Mb
GET BOOK

Description : This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.


Transcendental Number Theory

Author by : Alan Baker
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 13
Total Download : 181
File Size : 48,9 Mb
GET BOOK

Description : First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.


Number Theory Iv

Author by : A.N. Parshin
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 85
Total Download : 169
File Size : 48,9 Mb
GET BOOK

Description : This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.


Analytic Number Theory

Author by : B. Berndt
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 29
Total Download : 939
File Size : 53,6 Mb
GET BOOK

Description : On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fifty-four talks, including ten in vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H. L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R. C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory.


Pillars Of Transcendental Number Theory

Author by : Saradha Natarajan
Languange : en
Publisher by : Springer Nature
Format Available : PDF, ePub, Mobi
Total Read : 55
Total Download : 419
File Size : 55,9 Mb
GET BOOK

Description : This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite–Lindemann–Weierstrass theorem, Gelfond–Schneider theorem, Schmidt’s subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker’s original results. This book presents Baker’s original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of “Exercises” and interesting information presented as “Notes,” intended to spark readers’ curiosity.


Diophantine Approximation

Author by : David Masser
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 44
Total Download : 916
File Size : 55,8 Mb
GET BOOK

Description : Diophantine Approximation is a branch of Number Theory having its origins intheproblemofproducing“best”rationalapproximationstogivenrealn- bers. Since the early work of Lagrange on Pell’s equation and the pioneering work of Thue on the rational approximations to algebraic numbers of degree ? 3, it has been clear how, in addition to its own speci?c importance and - terest, the theory can have fundamental applications to classical diophantine problems in Number Theory. During the whole 20th century, until very recent times, this fruitful interplay went much further, also involving Transcend- tal Number Theory and leading to the solution of several central conjectures on diophantine equations and class number, and to other important achie- ments. These developments naturally raised further intensive research, so at the moment the subject is a most lively one. This motivated our proposal for a C. I. M. E. session, with the aim to make it available to a public wider than specialists an overview of the subject, with special emphasis on modern advances and techniques. Our project was kindly supported by the C. I. M. E. Committee and met with the interest of a largenumberofapplicants;forty-twoparticipantsfromseveralcountries,both graduatestudentsandseniormathematicians,intensivelyfollowedcoursesand seminars in a friendly and co-operative atmosphere. The main part of the session was arranged in four six-hours courses by Professors D. Masser (Basel), H. P. Schlickewei (Marburg), W. M. Schmidt (Boulder) and M. Waldschmidt (Paris VI). This volume contains expanded notes by the authors of the four courses, together with a paper by Professor Yu. V.


Algebraic Number Theory And Diophantine Analysis

Author by : F. Halter-Koch
Languange : en
Publisher by : Walter de Gruyter
Format Available : PDF, ePub, Mobi
Total Read : 35
Total Download : 970
File Size : 55,6 Mb
GET BOOK

Description : The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.


Spectral Theory Of Differential Operators

Author by : I.W. Knowles
Languange : en
Publisher by : Elsevier
Format Available : PDF, ePub, Mobi
Total Read : 63
Total Download : 578
File Size : 44,9 Mb
GET BOOK

Description : Spectral Theory of Differential Operators


Class Groups Of Number Fields And Related Topics

Author by : Kalyan Chakraborty
Languange : en
Publisher by : Springer Nature
Format Available : PDF, ePub, Mobi
Total Read : 41
Total Download : 589
File Size : 55,9 Mb
GET BOOK

Description : This book gathers original research papers and survey articles presented at the “International Conference on Class Groups of Number Fields and Related Topics,” held at Harish-Chandra Research Institute, Allahabad, India, on September 4–7, 2017. It discusses the fundamental research problems that arise in the study of class groups of number fields and introduces new techniques and tools to study these problems. Topics in this book include class groups and class numbers of number fields, units, the Kummer–Vandiver conjecture, class number one problem, Diophantine equations, Thue equations, continued fractions, Euclidean number fields, heights, rational torsion points on elliptic curves, cyclotomic numbers, Jacobi sums, and Dedekind zeta values. This book is a valuable resource for undergraduate and graduate students of mathematics as well as researchers interested in class groups of number fields and their connections to other branches of mathematics. New researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.


Algebraic Geometry Santa Cruz 1995

Author by : János Kollár
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 23
Total Download : 352
File Size : 54,7 Mb
GET BOOK

Description : This volume contains many of the lectures delivered at the AMS Summer Research Institute on Algebraic Geometry held at the University of California, Santa Cruz, in July 1995. The aim of the conference was to provide a comprehensive view of the development of algebraic geometry in the past decade and to lay special emphasis on emerging new directions. The focus of the papers in these volumes is on expository surveys of important areas rather than on technical presentations of new results. This book is intended for graduate students and research mathematicains interested in algebraic geometry and related areas.


Lectures On Contact 3 Manifolds Holomorphic Curves And Intersection Theory

Author by : Chris Wendl
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 93
Total Download : 991
File Size : 44,5 Mb
GET BOOK

Description : Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions. Siefring's recent extension of the theory to punctured holomorphic curves allowed similarly important results for contact 3-manifolds and their symplectic fillings. Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology. The appendices provide valuable information for researchers, including a concise reference guide on Siefring's theory and a self-contained proof of a weak version of the Micallef-White theorem.


The Random Matrix Theory Of The Classical Compact Groups

Author by : Elizabeth S. Meckes
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 17
Total Download : 681
File Size : 54,6 Mb
GET BOOK

Description : This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.


Number Theory In Progress

Author by : Kálmán Györy
Languange : en
Publisher by : Walter de Gruyter
Format Available : PDF, ePub, Mobi
Total Read : 93
Total Download : 288
File Size : 41,7 Mb
GET BOOK

Description : Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997.


Unit Equations In Diophantine Number Theory

Author by : Jan-Hendrik Evertse
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 21
Total Download : 318
File Size : 45,5 Mb
GET BOOK

Description : Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.


Periods And Special Functions In Transcendence

Author by : Tretkoff Paula B
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 94
Total Download : 912
File Size : 55,5 Mb
GET BOOK

Description : This book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi–Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.


Number Theory

Author by : Source Wikipedia
Languange : en
Publisher by : University-Press.org
Format Available : PDF, ePub, Mobi
Total Read : 74
Total Download : 285
File Size : 50,5 Mb
GET BOOK

Description : Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 231. Chapters: Natural number, Euler's totient function, P-adic number, Coprime, Factorial, Euclid, List of mathematical functions, Fundamental theorem of arithmetic, Algebraic number, Linear congruence theorem, Proofs of Fermat's little theorem, Bernoulli number, Collatz conjecture, Euler's sum of powers conjecture, Fermat number, Quadratic reciprocity, Catalan's conjecture, Square-free integer, Golomb ruler, Unique factorization domain, Amicable number, Partition, Sierpinski number, Langlands program, Faltings' theorem, List of number theory topics, Cyclotomic polynomial, Fermat's Last Theorem, Proof of Fermat's Last Theorem for specific exponents, Weil conjectures, Ideal lattice cryptography, Ramanujan's sum, Quartic reciprocity, Wiles' proof of Fermat's Last Theorem, Egyptian fraction, Normal number, Formulas for generating Pythagorean triples, Lindemann-Weierstrass theorem, Sylvester's sequence, Schoof's algorithm, Analytic number theory, Abc conjecture, Divisor function, Auxiliary function, Farey sequence, Greedy algorithm for Egyptian fractions, Bernoulli polynomials, Stern-Brocot tree, Basel problem, Birch and Swinnerton-Dyer conjecture, Stormer's theorem, Pentagonal number theorem, Sparse ruler, Harmonic number, Elliptic divisibility sequence, Znam's problem, Paley graph, Skewes' number, Coin problem, Quote notation, Vieta jumping, Schanuel's conjecture, Euler product, Digital root, Diophantine approximation, Squared triangular number, Cube, Lychrel number, Hecke character, Bertrand's postulate, Tau-function, Ducci sequence, Ostrowski's theorem, Cyclic number, Taxicab number, Multiplicative partition, Congruent number, Cunningham project, Automorphic form, Q-Pochhammer symbol, Neron-Tate height, Ideal number, Euclid's lemma, Zeckendorf's theorem, Smarandache function, Disquisitiones Arithmeticae, Natural...


Matrix Positivity

Author by : Charles R. Johnson
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 64
Total Download : 301
File Size : 44,9 Mb
GET BOOK

Description : Matrix positivity is a central topic in matrix theory: properties that generalize the notion of positivity to matrices arose from a large variety of applications, and many have also taken on notable theoretical significance, either because they are natural or unifying. This is the first book to provide a comprehensive and up-to-date reference of important material on matrix positivity classes, their properties, and their relations. The matrix classes emphasized in this book include the classes of semipositive matrices, P-matrices, inverse M-matrices, and copositive matrices. This self-contained reference will be useful to a large variety of mathematicians, engineers, and social scientists, as well as graduate students. The generalizations of positivity and the connections observed provide a unique perspective, along with theoretical insight into applications and future challenges. Direct applications can be found in data analysis, differential equations, mathematical programming, computational complexity, models of the economy, population biology, dynamical systems and control theory.


Coarse Geometry Of Topological Groups

Author by : Christian Rosendal
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 80
Total Download : 985
File Size : 45,5 Mb
GET BOOK

Description : Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.


Assouad Dimension And Fractal Geometry

Author by : Jonathan M. Fraser
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 62
Total Download : 326
File Size : 53,5 Mb
GET BOOK

Description : The Assouad dimension is a notion of dimension in fractal geometry that has been the subject of much interest in recent years. This book, written by a world expert on the topic, is the first thorough account of the Assouad dimension and its many variants and applications in fractal geometry and beyond. It places the theory of the Assouad dimension in context among up-to-date treatments of many key advances in fractal geometry, while also emphasising its diverse connections with areas of mathematics including number theory, dynamical systems, harmonic analysis, and probability theory. A final chapter detailing open problems and future directions for research brings readers to the cutting edge of this exciting field. This book will be an indispensable part of the modern fractal geometer's library and a valuable resource for pure mathematicians interested in the beauty and many applications of the Assouad dimension.


Attractors Of Hamiltonian Nonlinear Partial Differential Equations

Author by : Alexander Komech
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 70
Total Download : 981
File Size : 48,6 Mb
GET BOOK

Description : This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.


Operator Analysis

Author by : Jim Agler
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 57
Total Download : 828
File Size : 45,5 Mb
GET BOOK

Description : This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.


Rational Points On Elliptic Curves

Author by : Joseph H. Silverman
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 29
Total Download : 185
File Size : 42,7 Mb
GET BOOK

Description : The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.