Problems in Algebraic Number Theory
Title | Problems in Algebraic Number Theory PDF eBook |
Author | M. Ram Murty |
Publisher | Springer Science & Business Media |
Pages | 354 |
Release | 2005-09-28 |
Genre | Mathematics |
ISBN | 0387269983 |
The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
Steps into Analytic Number Theory
Title | Steps into Analytic Number Theory PDF eBook |
Author | Paul Pollack |
Publisher | Springer Nature |
Pages | 191 |
Release | 2021-02-08 |
Genre | Mathematics |
ISBN | 3030650774 |
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.
A Course in Analytic Number Theory
Title | A Course in Analytic Number Theory PDF eBook |
Author | Marius Overholt |
Publisher | American Mathematical Soc. |
Pages | 394 |
Release | 2014-12-30 |
Genre | Mathematics |
ISBN | 1470417065 |
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.
Analytic Number Theory
Title | Analytic Number Theory PDF eBook |
Author | Donald J. Newman |
Publisher | Springer Science & Business Media |
Pages | 80 |
Release | 2006-04-18 |
Genre | Mathematics |
ISBN | 0387227407 |
Some of the central topics in number theory, presnted in a simple and concise fashion. The author covers an amazing amount of material, despite a leisurely pace and emphasis on readability. His heartfelt enthusiasm enables readers to see what is magical about the subject. All the topics are presented in a refreshingly elegant and efficient manner with clever examples and interesting problems throughout. The text is suitable for a graduate course in analytic number theory.
A Primer of Analytic Number Theory
Title | A Primer of Analytic Number Theory PDF eBook |
Author | Jeffrey Stopple |
Publisher | Cambridge University Press |
Pages | 404 |
Release | 2003-06-23 |
Genre | Mathematics |
ISBN | 9780521012539 |
An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
Analytic Number Theory
Title | Analytic Number Theory PDF eBook |
Author | P. T. Bateman |
Publisher | World Scientific |
Pages | 378 |
Release | 2004 |
Genre | Mathematics |
ISBN | 9789812560803 |
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/
Abstract analytic number theory
Title | Abstract analytic number theory PDF eBook |
Author | Knopfmacher |
Publisher | Newnes |
Pages | 333 |
Release | 2009-02-04 |
Genre | Technology & Engineering |
ISBN | 0444107797 |
North-Holland Mathematical Library, Volume 12: Abstract Analytic Number Theory focuses on the approaches, methodologies, and principles of the abstract analytic number theory. The publication first deals with arithmetical semigroups, arithmetical functions, and enumeration problems. Discussions focus on special functions and additive arithmetical semigroups, enumeration and zeta functions in special cases, infinite sums and products, double series and products, integral domains and arithmetical semigroups, and categories satisfying theorems of the Krull-Schmidt type. The text then ponders on semigroups satisfying Axiom A, asymptotic enumeration and "statistical" properties of arithmetical functions, and abstract prime number theorem. Topics include asymptotic properties of prime-divisor functions, maximum and minimum orders of magnitude of certain functions, asymptotic enumeration in certain categories, distribution functions of prime-independent functions, and approximate average values of special arithmetical functions. The manuscript takes a look at arithmetical formations, additive arithmetical semigroups, and Fourier analysis of arithmetical functions, including Fourier theory of almost even functions, additive abstract prime number theorem, asymptotic average values and densities, and average values of arithmetical functions over a class. The book is a vital reference for researchers interested in the abstract analytic number theory.