Steps into Analytic Number Theory
A Problem-Based Introduction
Authors: Pollack, Paul, Singha Roy, Akash
Free Preview- Challenges students ranging from high school to graduate levels to develop problem-solving skills in analytic number theory
- Balances elementary yet ingenious problems with applications not usually seen in classes
- Suitable as a rich supplementary text in Analytic Number Theory for undergraduate and graduate courses
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- About this Textbook
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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.
- About the authors
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Paul Pollack is a Professor at the University of Georgia, USA.
Akash Singha Roy is an undergraduate student at the Chennai Mathematical Institute, India. - Reviews
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“This book is much more advanced and makes heavy use of complex analysis. … This is an excellent and probably unique introduction to the use of continuous methods in the discrete world of number theory, and accessible to a wide mathematical audience.” (Allen Stenger, MAA Reviews, June 20, 2021)
- Table of contents (31 chapters)
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Step #1
Pages 1-3
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Step #2
Pages 5-7
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Step #3
Pages 9-11
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Step #4
Pages 13-15
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Step #5
Pages 17-20
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Table of contents (31 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Steps into Analytic Number Theory
- Book Subtitle
- A Problem-Based Introduction
- Authors
-
- Paul Pollack
- Akash Singha Roy
- Series Title
- Problem Books in Mathematics
- Copyright
- 2021
- Publisher
- Springer International Publishing
- Copyright Holder
- The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-65077-3
- DOI
- 10.1007/978-3-030-65077-3
- Hardcover ISBN
- 978-3-030-65076-6
- Series ISSN
- 0941-3502
- Edition Number
- 1
- Number of Pages
- XIII, 197
- Number of Illustrations
- 3 b/w illustrations
- Topics
