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Author : Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff
Publisher : Cambridge University Press
Page : 341 pages
File Size : 41,5 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781107552371
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
Author : Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff
Publisher : Unknown
Page : 321 pages
File Size : 40,5 Mb
Release : 2016
Category : Analytic functions
ISBN : 131681873X
Author : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 53,9 Mb
Release : 2018-06-15
Category : Mathematics
ISBN : 9783319749082
This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
Author : Dmitry A. Badziahin
Publisher : Unknown
Page : 0 pages
File Size : 44,8 Mb
Release : 2016
Category : Analytic functions
ISBN : 1316818853
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
Author : Danyal Sadik
Publisher : Unknown
Page : 255 pages
File Size : 40,8 Mb
Release : 2016-08-01
Category : Electronic
ISBN : 1681175657
"One might have thought that number theory was simply the study of numbers, but that is too broad a definition, since numbers are almost ubiquitous in mathematics. Number theory is a vast and fascinating field of mathematics, sometimes called ""higher arithmetic,"" consisting of the study of the properties of whole numbers. Primes and prime factorization are especially important in number theory, as are a number of functions such as the divisor function, Riemann zeta function, and totient function. Analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. Analytic number theory, and its applications and interactions, are currently experiencing intensive progress, in sometimes unexpected directions. In recent years, many important classical questions have seen spectacular advances based on new techniques; conversely, methods developed in analytic number theory have led to the solution of striking problems in other fields. Recent advances in analytic number theory have had repercussions in various mathematical subjects, such as harmonic analysis, ergodic theory and dynamics, additive and multiplicative combinatorics and theoretical computer science. The biggest technical change after 1950 has been the development of sieve methods, particularly in multiplicative problems. These are combinatorial in nature, and quite varied. The extremal branch of combinatorial theory has in return been greatly influenced by the value placed in analytic number theory on quantitative upper and lower bounds. Another recent development is probabilistic number theory, which uses methods from probability theory to estimate the distribution of number theoretic functions, such as how many prime divisors a number has. Problems in Analytic Number Theory present a problem-solving approach to the difficult subject of analytic number theory. This book is focused at researchers, teachers, and graduate students interested in number theory and its links with other branches of science."
Author : M. M. Dodson
Publisher : Cambridge University Press
Page : 185 pages
File Size : 49,9 Mb
Release : 1989-11-09
Category : Mathematics
ISBN : 9780521369190
This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.
Author : Valentin Blomer,Preda Mihăilescu
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 55,5 Mb
Release : 2011-11-19
Category : Mathematics
ISBN : 9781461412199
The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed from lectures given at the "International Conference on the Occasion of the 60th Birthday of S. J. Patterson", held at the University Göttingen, July 27-29 2009. Many of the included chapters have been contributed by invited participants. This volume presents and investigates the most recent developments in various key topics in analytic number theory and several related areas of mathematics. The volume is intended for graduate students and researchers of number theory as well as applied mathematicians interested in this broad field.
Author : Henryk Iwaniec,Emmanuel Kowalski
Publisher : American Mathematical Soc.
Page : 615 pages
File Size : 51,9 Mb
Release : 2021-10-14
Category : Education
ISBN : 9781470467708
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Author : A. G. Postnikov
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 53,9 Mb
Release : 1988-12-31
Category : Mathematics
ISBN : 9780821813492
Aimed at a level between textbooks and the latest research monographs, this book is directed at researchers, teachers, and graduate students interested in number theory and its connections with other branches of science. Choosing to emphasize topics not sufficiently covered in the literature, the author has attempted to give as broad a picture as possible of the problems of analytic number theory.
Author : Thomas Hagen,Florian Rupp,Jrgen Scheurle
Publisher : World Scientific
Page : 279 pages
File Size : 42,5 Mb
Release : 2016
Category : Mathematics
ISBN : 9789814699877
"This volume consists of a selection of research-type articles on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between theoretical and more applied work, thus spanning the chasm between abstract insight and actual application. Several of the articles are expected to be in the intersection of dynamical systems theory and number theory. One article will likely relate the topics presented to the academic achievements and interests of Prof. Leutbecher and shed light on common threads among all the contributions."--
Author : Marius Overholt
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 48,8 Mb
Release : 2014-12-30
Category : Mathematics
ISBN : 9781470417062
This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.
Author : Bateman Paul Trevier,Diamond Harold G
Publisher : World Scientific
Page : 376 pages
File Size : 53,5 Mb
Release : 2004-09-07
Category : Mathematics
ISBN : 9789814365567
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at www.math.uiuc.edu/~diamond/.
Author : Pieter Moree,Anke Pohl,L’ubomír Snoha,Tom Ward
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 41,6 Mb
Release : 2020-02-12
Category : Education
ISBN : 9781470451004
This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Author : J. B. Friedlander,D.R. Heath-Brown,H. Iwaniec,J. Kaczorowski
Publisher : Springer
Page : 217 pages
File Size : 55,9 Mb
Release : 2006-11-10
Category : Mathematics
ISBN : 9783540363644
The four papers collected in this book discuss advanced results in analytic number theory, including recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials; counting integer solutions to Diophantine equations, using results from algebraic geometry and the geometry of numbers; the theory of Siegel’s zeros and of exceptional characters of L-functions; and an up-to-date survey of the axiomatic theory of L-functions introduced by Selberg.
Author : Heng Huat Chan
Publisher : World Scientific Publishing Company
Page : 128 pages
File Size : 43,6 Mb
Release : 2009-04-21
Category : Mathematics
ISBN : 9789814365277
This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression. The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.
