The Large Sieve And Its Applications

Author by : E. Kowalski
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 47
Total Download : 392
File Size : 55,9 Mb
GET BOOK

Description : Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.


Number Theory And Its Applications In China

Author by : Yuan Wang
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 28
Total Download : 933
File Size : 42,6 Mb
GET BOOK

Description : Of all modern mathematical forms, number theory is one of the earliest to be explored in China and is the one to which the Chinese have made their greatest contributions. Yan Wu-zhi first introduced number theory into China in the 1920s. Particularly influential in the field was Hua Loo-keng, who studied with G. H. Hardy and made significant contributions in the areas estimating complete exponential sums, Waring's problems, Tarry's problems, and Vinogradov's method. Interest in number theory continued to flourish following the founding of the People's Republic of China. The most noted accomplishments by Chinese mathematicians were focused on the solution of Goldbach's Conjecture and on the sieve method. Although the Cultural Revolution interrupted research in number theory for more than 10 years, the field is now growing in China.A number of universities now have advanced programs in the subject and a wide variety of topics, including the applications of number theory. This volume contains nine survey articles and three articles on current research. The collection emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. The collection is intended not only to survey the significant contributions of Chinese mathematicians, but also to reflect the latest developments and current state of research in number theory in China.


An Introduction To Sieve Methods And Their Applications

Author by : Alina Carmen Cojocaru
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 20
Total Download : 532
File Size : 49,9 Mb
GET BOOK

Description : Rather than focus on the technical details which can obscure the beauty of sieve theory, the authors focus on examples and applications, developing the theory in parallel.


Number Theory And Its Applications

Author by : Cem Y. Yildrim
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 10
Total Download : 682
File Size : 40,6 Mb
GET BOOK

Description : This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey.


An Introduction To Probabilistic Number Theory

Author by : Emmanuel Kowalski
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 74
Total Download : 146
File Size : 42,8 Mb
GET BOOK

Description : This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.


Goldbach Conjecture

Author by : Yuan Wang
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 18
Total Download : 149
File Size : 53,9 Mb
GET BOOK

Description : This book provides a detailed description of a most important unsolved mathematical problem ? the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920's. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture.


Thin Groups And Superstrong Approximation

Author by : Emmanuel Breuillard
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 94
Total Download : 384
File Size : 40,5 Mb
GET BOOK

Description : Based on the workshop "Thin Groups and Super-strong Approximation,'' held at Mathematical Sciences Research Institute, February 6th through 10th, 201


Rational Number Theory In The 20th Century

Author by : Władysław Narkiewicz
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 60
Total Download : 163
File Size : 53,5 Mb
GET BOOK

Description : The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.


Sieve Methods

Author by : Heine Halberstam
Languange : en
Publisher by : Courier Corporation
Format Available : PDF, ePub, Mobi
Total Read : 75
Total Download : 484
File Size : 54,6 Mb
GET BOOK

Description : This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition.


Computational Science And Its Applications Iccsa 2014

Author by : Beniamino Murgante
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 36
Total Download : 497
File Size : 40,9 Mb
GET BOOK

Description : The six-volume set LNCS 8579-8584 constitutes the refereed proceedings of the 14th International Conference on Computational Science and Its Applications, ICCSA 2014, held in Guimarães, Portugal, in June/July 2014. The 347 revised papers presented in 30 workshops and a special track were carefully reviewed and selected from 1167. The 289 papers presented in the workshops cover various areas in computational science ranging from computational science technologies to specific areas of computational science such as computational geometry and security.


Probabilistic Number Theory I

Author by : P.D.T.A. Elliott
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 85
Total Download : 326
File Size : 45,6 Mb
GET BOOK

Description : In 1791 Gauss made the following assertions (collected works, Vol. 10, p.ll, Teubner, Leipzig 1917): Primzahlen unter a (= 00) a la Zahlen aus zwei Factoren lla· a la (warsch.) aus 3 Factoren 1 (lla)2a -- 2 la et sic in info In more modern notation, let 1tk(X) denote the number of integers not exceeding x which are made up of k distinct prime factors, k = 1, 2 ... Then his assertions amount to the asymptotic estimate x (log log X)k-l () 1tk X '"--"';"'-"--"::--:-'-, - (x-..oo). log x (k-1)! The case k = 1, known as the Prime Number Theorem, was independently established by Hadamard and de la Vallee Poussin in 1896, just over a hundred years later. The general case was deduced by Landau in 1900; it needs only an integration by parts. Nevertheless, one can scarcely say that Probabilistic Number Theory began with Gauss. In 1914 the Indian original mathematician Srinivasa Ramanujan arrived in England. Six years of his short life remained to him during which he wrote, amongst other things, five papers and two notes jointly with G.H. Hardy.


Automorphic Representations L Functions And Applications

Author by : Stephen Rallis
Languange : en
Publisher by : Walter de Gruyter
Format Available : PDF, ePub, Mobi
Total Read : 74
Total Download : 327
File Size : 54,8 Mb
GET BOOK

Description : Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.


Groups St Andrews 2013

Author by : C. M. Campbell
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 23
Total Download : 918
File Size : 49,7 Mb
GET BOOK

Description : Leading researchers survey the latest developments in group theory and many related areas.


There Are Tittles In This Title

Author by : Mitchell Symons
Languange : en
Publisher by : Michael O'Mara Books
Format Available : PDF, ePub, Mobi
Total Read : 15
Total Download : 981
File Size : 41,8 Mb
GET BOOK

Description : Did you know that 'Almost' is the longest word in the English language with all the letters in alphabetical order? Or that 'Stewardesses' is the longest word you can type solely with your left hand? Or that fireflies aren't flies, they're beetles? From information about words and their uses, useful lists of things you never knew had names, palindromes, famous lines from literature and film, to bizarre test answers and much, much more, There Are Tittles in This Title is bursting with truly oddball facts about words and language - and will have you hooked from the very first page.


Complexity And Randomness In Group Theory

Author by : Frédérique Bassino
Languange : en
Publisher by : Walter de Gruyter GmbH & Co KG
Format Available : PDF, ePub, Mobi
Total Read : 57
Total Download : 812
File Size : 53,6 Mb
GET BOOK

Description : This book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.


The Weird World Of Words

Author by : Mitchell Symons
Languange : en
Publisher by : Houghton Mifflin Harcourt
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 315
File Size : 40,6 Mb
GET BOOK

Description : A collection of English-language trivia shares fun facts about words and language usage, from "almost" being the longest English word with its letters in alphabetical order to "stewardesses" being the longest word typed with the left hand. Original. 10,000 first printing.


The Bumper Book For The Loo

Author by : Mitchell Symons
Languange : en
Publisher by : Random House
Format Available : PDF, ePub, Mobi
Total Read : 71
Total Download : 518
File Size : 41,8 Mb
GET BOOK

Description : When Mitchell Symons wrote his extraordinary bestsellers This Book, That Book and The Other Book - all neatly combined in one sensational volume, The Ultimate Loo Book - he was judged by many to be the King of Trivia. Now, inThe Bumper Book for the Loo, this supremo of weird and wonderful, astonishing and inexplicable facts, figures, stats and stories returns with a super selection of trivialistic treats - each one more remarkable and, yes, even more trivial than anything he's compiled before. For example, did you know that... ·The first alarm clock could only ring at 4 a.m... ·There was once an internet rumour that Belgium doesn't exist... ·In 1830, King Louis XIX ruled France for just 15 minutes... ·All mammals have jaws but only humans have chins... ·Peru has more pyramids than Egypt... Packed to the rafters with all manner of useful and useless information, lists of the biggest, the smallest, the best and the worst, The Bumper Book for the Loo is a hilarious compendium of endless delights - and a hugely entertaining, unputdownable feat of nonsense!


Group Cohomology And Algebraic Cycles

Author by : Burt Totaro
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 20
Total Download : 454
File Size : 42,9 Mb
GET BOOK

Description : Group cohomology reveals a deep relationship between algebra and topology, and its recent applications have provided important insights into the Hodge conjecture and algebraic geometry more broadly. This book presents a coherent suite of computational tools for the study of group cohomology and algebraic cycles. Early chapters synthesize background material from topology, algebraic geometry, and commutative algebra so readers do not have to form connections between the literatures on their own. Later chapters demonstrate Peter Symonds's influential proof of David Benson's regularity conjecture, offering several new variants and improvements. Complete with concrete examples and computations throughout, and a list of open problems for further study, this book will be valuable to graduate students and researchers in algebraic geometry and related fields.


Canonical Ramsey Theory On Polish Spaces

Author by : Vladimir Kanovei
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 51
Total Download : 549
File Size : 47,8 Mb
GET BOOK

Description : This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and Gandy–Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.


A Universal Construction For Groups Acting Freely On Real Trees

Author by : Ian Chiswell
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 10
Total Download : 713
File Size : 50,9 Mb
GET BOOK

Description : The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.


Modern Approaches To The Invariant Subspace Problem

Author by : Isabelle Chalendar
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 11
Total Download : 179
File Size : 41,5 Mb
GET BOOK

Description : One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.


Singularities Of The Minimal Model Program

Author by : János Kollár
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 22
Total Download : 543
File Size : 52,7 Mb
GET BOOK

Description : This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.


Malliavin Calculus For L Vy Processes And Infinite Dimensional Brownian Motion

Author by : Horst Osswald
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 33
Total Download : 290
File Size : 54,6 Mb
GET BOOK

Description : After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.


Ridge Functions

Author by : Allan Pinkus
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 76
Total Download : 683
File Size : 55,9 Mb
GET BOOK

Description : Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.