Analytic Number Theory An Introductory Course
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Analytic Number Theory
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Author : P. T. Bateman
language : en
Publisher: World Scientific
Release Date : 2004
Analytic Number Theory written by P. T. Bateman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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 http: //www.math.uiuc.edu/ diamond/
Analytic Number Theory An Introductory Course
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Author : Bateman Paul Trevier
language : en
Publisher: World Scientific
Release Date : 2004-09-07
Analytic Number Theory An Introductory Course written by Bateman Paul Trevier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-07 with Mathematics categories.
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/.
A Course In Analytic Number Theory
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Author : Marius Overholt
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-30
A Course In Analytic Number Theory written by Marius Overholt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.
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.
Introduction To Analytic Number Theory
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Author : Tom M. Apostol
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Introduction To Analytic Number Theory written by Tom M. Apostol and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS
Steps Into Analytic Number Theory
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Author : Paul Pollack
language : en
Publisher: Springer Nature
Release Date : 2021-02-08
Steps Into Analytic Number Theory written by Paul Pollack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-08 with Mathematics categories.
This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.
Introduction To P Adic Analytic Number Theory
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Author : M. Ram Murty
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-02-09
Introduction To P Adic Analytic Number Theory written by M. Ram Murty and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Number theory categories.
This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.
Introduction To Analytic Number Theory
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Author : Komaravolu Chandrasekharan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Analytic Number Theory written by Komaravolu Chandrasekharan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book has grown out of a course of lectures I have given at the Eidgenossische Technische Hochschule, Zurich. Notes of those lectures, prepared for the most part by assistants, have appeared in German. This book follows the same general plan as those notes, though in style, and in text (for instance, Chapters III, V, VIII), and in attention to detail, it is rather different. Its purpose is to introduce the non-specialist to some of the fundamental results in the theory of numbers, to show how analytical methods of proof fit into the theory, and to prepare the ground for a subsequent inquiry into deeper questions. It is pub lished in this series because of the interest evinced by Professor Beno Eckmann. I have to acknowledge my indebtedness to Professor Carl Ludwig Siegel, who has read the book, both in manuscript and in print, and made a number of valuable criticisms and suggestions. Professor Raghavan Narasimhan has helped me, time and again, with illuminating comments. Dr. Harold Diamond has read the proofs, and helped me to remove obscurities. I have to thank them all. K.C.
Introduction To Analytic Number Theory
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Author : A. G. Postnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 1988-12-31
Introduction To Analytic Number Theory written by A. G. Postnikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-31 with Mathematics categories.
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.
Introduction To Analytic And Probabilistic Number Theory
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Author : G. Tenenbaum
language : en
Publisher: Cambridge University Press
Release Date : 1995-06-30
Introduction To Analytic And Probabilistic Number Theory written by G. Tenenbaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-06-30 with Mathematics categories.
This is a self-contained introduction to analytic methods in number theory, assuming on the part of the reader only what is typically learned in a standard undergraduate degree course. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians. These aspects are aided by the inclusion at the end of each chapter a section of bibliographic notes and detailed exercises.
Problems In Analytic Number Theory
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Author : U.S.R. Murty
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Problems In Analytic Number Theory written by U.S.R. Murty and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
"In order to become proficient in mathematics, or in any subject," writes Andre Weil, "the student must realize that most topics in volve only a small number of basic ideas. " After learning these basic concepts and theorems, the student should "drill in routine exercises, by which the necessary reflexes in handling such concepts may be ac quired. . . . There can be no real understanding of the basic concepts of a mathematical theory without an ability to use them intelligently and apply them to specific problems. " Weil's insightfulobservation becomes especially important at the graduate and research level. It is the viewpoint of this book. Our goal is to acquaint the student with the methods of analytic number theory as rapidly as possible through examples and exercises. Any landmark theorem opens up a method of attacking other problems. Unless the student is able to sift out from the mass of theory the underlying techniques, his or her understanding will only be academic and not that of a participant in research. The prime number theorem has given rise to the rich Tauberian theory and a general method of Dirichlet series with which one can study the asymptotics of sequences. It has also motivated the development of sieve methods. We focus on this theme in the book. We also touch upon the emerging Selberg theory (in Chapter 8) and p-adic analytic number theory (in Chapter 10).