Steps into Analytic Number Theory 解析数论的步骤：基于问题的导论 Paul Pollack; Akash Singha Roy

基本信息

Format:Paperback / softback 197 pages, 3 Illustrations, black and white; XIII, 197 p. 3 illus.

Publisher:Springer Nature Switzerland AG

Imprint:Springer Nature Switzerland AG

Edition:1st ed. 2021

ISBN:9783030650797

Published:10 Feb 2022

Classifications:Teaching of a specific subject, Number theory

Readership:Professional & Vocational

Weight:332g

Dimensions:155 x 235 x 15 (mm)

基本信息仅供参考，具体以实物为准

书籍简介

这本问题集汇集了15个关于解析数论的问题集，从高中生到研究生都可以从中获益。本书源自作者在2019年7月7日至8月9日于中国镇江举办的罗斯/亚洲数学项目中讲授的为期5周的课程。虽然建议读者具备扎实的数学解题背景（如参加数学竞赛的训练），但并不假定读者拥有高级学科知识。

大多数解题方法只要求掌握基本数论和微积分知识。问题涉及一些关键主题，如算术函数的值分布、素数的分布、素数模的平方和非平方的分布、关于算术级数中素数的狄利克特定理等。本书适合任何对发展解析数论解题技巧特别感兴趣的学生。

作为本科生和研究生的解析数论入门课程的辅助教材，它将成为讲师和学生的宝贵助手。

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.

作者简介

保罗-波拉克是美国佐治亚大学教授。

Akash Singha Roy 是印度钦奈数学学院的本科生。

Paul Pollack is a Professor at the University of Georgia, USA.

Akash Singha Roy is an undergraduate student at the Chennai Mathematical Institute, India.