Introduction to Analytic Number Theory PDF Download
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Author: Tom M. Apostol
Publisher: Springer Science & Business Media
ISBN: 1475755791
Category : Mathematics
Languages : en
Pages : 352
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Book Description
"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
Author: Tom M. Apostol
Publisher: Springer Science & Business Media
ISBN: 1475755791
Category : Mathematics
Languages : en
Pages : 352
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Book Description
"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
Author: Raymond George Ayoub
Publisher: Amer Mathematical Society
ISBN: 9780821841815
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This book is divided into five chapters: I. Dirichlet's theorem on primes in an arithmetic progression; II. Distribution of primes; III. The theory of partitions; IV. Waring's problem; V. Dirichlet L-functions and class number of quadratic fields.
Author: Raymond George Ayoub
Publisher: Eurospan
ISBN:
Category : Mathematical analysis
Languages : en
Pages : 402
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Book Description
The mathematical preparation is relatively modest: the elements of number theory, algebra, and group theory are required. A good working knowledge of element of complex function theory and general analytic processes is needed. The subject matter is of varying difficulty, and while the first chapter reads relatively easily, subsequent chapters require close attention. The subject of analytic number theory is not clearly defined. While the choice of topics included herein is somewhat arbitrary, the topics themselves represent some important problems of number theory to which generations of outstanding mathematicians have contributed.
Author: G. Tenenbaum
Publisher: Cambridge University Press
ISBN: 9780521412612
Category : Mathematics
Languages : en
Pages : 180
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Book Description
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.
Author: P. T. Bateman
Publisher: World Scientific
ISBN: 9789812560803
Category : Mathematics
Languages : en
Pages : 378
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Book Description
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/
Author: Jeffrey Stopple
Publisher: Cambridge University Press
ISBN: 9780521012539
Category : Mathematics
Languages : en
Pages : 404
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Book Description
An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
Author: M. Ram Murty
Publisher: American Mathematical Soc.
ISBN: 0821847740
Category : Mathematics
Languages : en
Pages : 162
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Book Description
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.
Author: Henryk Iwaniec
Publisher: American Mathematical Soc.
ISBN: 1470467704
Category : Education
Languages : en
Pages : 615
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Book Description
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: Paul Pollack
Publisher: Springer Nature
ISBN: 3030650774
Category : Mathematics
Languages : en
Pages : 191
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Book Description
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.
Author:
Publisher:
ISBN: 9787115156112
Category : Number theory
Languages : zh-CN
Pages : 435
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Book Description
本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。
