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Author : John B. Friedlander,Henryk Iwaniec
Publisher : American Mathematical Soc.
Page : 554 pages
File Size : 47,6 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780821869697
Author : John B. Friedlander,Henryk Iwaniec
Publisher : American Mathematical Soc.
Page : 554 pages
File Size : 48,5 Mb
Release : 2010-06-22
Category : Mathematics
ISBN : 9780821849705
This is a true masterpiece that will prove to be indispensable to the serious researcher for many years to come. --Enrico Bombieri, Institute for Advanced Study This is a truly comprehensive account of sieves and their applications, by two of the world's greatest authorities. Beginners will find a thorough introduction to the subject, with plenty of helpful motivation. The more practised reader will appreciate the authors' insights into some of the more mysterious parts of the theory, as well as the wealth of new examples. --Roger Heath-Brown, University of Oxford, Fellow of Royal Society This is a comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. Included is a wide range of applications, both to traditional questions such as those concerning primes, and to areas previously unexplored by sieve methods, such as elliptic curves, points on cubic surfaces and quantum ergodicity. New proofs are given also of some of the central theorems of analytic number theory; these proofs emphasize and take advantage of the applicability of sieve ideas. The book contains numerous comments which provide the reader with insight into the workings of the subject, both as to what the sieve can do and what it cannot do. The authors reveal recent developements by which the parity barrier can be breached, exposing golden nuggets of the subject, previously inaccessible. The variety in the topics covered and in the levels of difficulty encountered makes this a work of value to novices and experts alike, both as an educational tool and a basic reference.
Author : J. B. Friedlander ((John B.)),Henryk Iwaniec
Publisher : Unknown
Page : 527 pages
File Size : 55,8 Mb
Release : 2010
Category : Electronic
ISBN : 1470417669
Author : Sam Chow,Niclas Technau
Publisher : American Mathematical Society
Page : 86 pages
File Size : 48,5 Mb
Release : 2024-05-15
Category : Mathematics
ISBN : 9781470468798
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Author : Olivier Bordellès
Publisher : Springer Nature
Page : 782 pages
File Size : 49,9 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9783030549466
This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
Author : Emmanuel Breuillard,Hee Oh
Publisher : Cambridge University Press
Page : 375 pages
File Size : 40,5 Mb
Release : 2014-02-17
Category : Mathematics
ISBN : 9781107036857
This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics.
Author : Kevin Broughan
Publisher : Cambridge University Press
Page : 513 pages
File Size : 44,6 Mb
Release : 2017-11-02
Category : Mathematics
ISBN : 9781107197121
This second volume of two presents analytic equivalents to the Riemann hypothesis. Includes an extensive set of appendices.
Author : Olivier Ramaré
Publisher : Springer Nature
Page : 342 pages
File Size : 46,8 Mb
Release : 2022-03-03
Category : Mathematics
ISBN : 9783030731694
This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided “walks” invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin–Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at “higher ground”, where they will find opportunities for extensions and applications, such as the Selberg formula, Brun’s sieve, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area.
Author : János Pintz,András Biró,Kálmán Györy,Gergely Harcos,Miklós Simonovits,József Szabados
Publisher : Walter de Gruyter
Page : 418 pages
File Size : 44,9 Mb
Release : 2013-12-12
Category : Mathematics
ISBN : 9783110282429
Paul Turán, one of the greatest Hungarian mathematicians, was born 100 years ago, on August 18, 1910. To celebrate this occasion the Hungarian Academy of Sciences, the Alfréd Rényi Institute of Mathematics, the János Bolyai Mathematical Society and the Mathematical Institute of Eötvös Loránd University organized an international conference devoted to Paul Turán's main areas of interest: number theory, selected branches of analysis, and selected branches of combinatorics. The conference was held in Budapest, August 22-26, 2011. Some of the invited lectures reviewed different aspects of Paul Turán's work and influence. Most of the lectures allowed participants to report about their own work in the above mentioned areas of mathematics.
Author : Dimitris Koukoulopoulos
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 46,6 Mb
Release : 2020-07-28
Category : Education
ISBN : 9781470462857
Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem. Throughout, the emphasis has been placed on explaining the main ideas rather than the most general results available. As a result, several methods are presented in terms of concrete examples that simplify technical details, and theorems are stated in a form that facilitates the understanding of their proof at the cost of sacrificing some generality. Each chapter concludes with numerous exercises of various levels of difficulty aimed to exemplify the material, as well as to expose the readers to more advanced topics and point them to further reading sources.
Author : Hugh Montgomery,Ashkan Nikeghbali,Michael Th. Rassias
Publisher : Springer
Page : 298 pages
File Size : 48,5 Mb
Release : 2017-09-11
Category : Mathematics
ISBN : 9783319599694
Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.
Author : László Lovász,Imre Ruzsa,Vera T. Sós
Publisher : Springer Science & Business Media
Page : 714 pages
File Size : 43,7 Mb
Release : 2014-01-24
Category : Mathematics
ISBN : 9783642392863
Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments.
Author : Alina Bucur,David Zureick-Brown
Publisher : American Mathematical Soc.
Page : 248 pages
File Size : 50,5 Mb
Release : 2019-11-22
Category : Education
ISBN : 9781470437848
In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with SL2(Fq) and some of its subgroups as the key examples. The article by Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from ℓ-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic L-functions, and Mumford-Tate groups.
Author : Prapanpong Pongsriiam
Publisher : American Mathematical Society
Page : 402 pages
File Size : 53,7 Mb
Release : 2023-06-02
Category : Mathematics
ISBN : 9781470464448
This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this second edition, sieve methods and additive number theory. The book is self-contained and easy to follow. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes which include a chapter summary, open questions, historical background, and resources for further study. Since many topics in this book are not typically covered at such an accessible level, Analytic Number Theory for Beginners is likely to fill an important niche in today's selection of titles in this field.
Author : Kevin Broughan
Publisher : Cambridge University Press
Page : 706 pages
File Size : 47,9 Mb
Release : 2023-09-30
Category : Mathematics
ISBN : 9781009384773
This three-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 3 covers new arithmetic and analytic equivalences from numerous studies in the field, such as Rogers and Tao, and presents derivations which show whether the Riemann hypothesis is decidable.