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 indeveloping 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 Author
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

"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)

Book Information
ISBN 9783030650797
Author Paul Pollack
Format Paperback
Page Count 197
Imprint Springer Nature Switzerland AG
Publisher Springer Nature Switzerland AG