Steps into Analytic Number Theory

Released on by Paul Pollack
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  • Steps into Analytic Number Theory Book Detail

  • Author : Paul Pollack
  • Release Date : 2021-02-08
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 191
  • ISBN 13 : 3030650774
  • File Size : 64,64 MB
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Steps into Analytic Number Theory by Paul Pollack PDF Summary

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.

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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