Number Theory

Tradition and Modernization

  • Wenpeng Zhang
  • Yoshio Tanigawa
Part of the Developments in Mathematics book series (DEVM, volume 15)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Shigeki Akiyama
    Pages 1-10
  3. YoungJu Choie, Winfried Kohnen
    Pages 23-26
  4. Toshihiro Hadano, Yoshiyuki Kitaoka, Tomio Kubota, Michihiro Nozaki
    Pages 67-80
  5. Shigeru Kanemitsu, Yoshio Tanigawa, Haruo Tsukada, Masami Yoshimoto
    Pages 103-118
  6. Katsuya Miyake
    Pages 175-183
  7. Zhi-Wei Sun
    Pages 205-218
  8. Wenguang Zhai
    Pages 219-227
  9. Back Matter
    Pages 239-241

About these proceedings

Introduction

Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. Though the topics and descriptive details appear varied, they are unified by two underlying principles: first, making everything readable as a book, and second, making a smooth transition from traditional approaches to modern ones by providing a rich array of examples.

The chapters are presented in quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the developments of number theory. Thus, on the one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated. The book emphasizes a few common features such as functional equations for various zeta-functions, modular forms, congruence conditions, exponential sums, and algorithmic aspects.

 

Audience

This book is intended for researchers and graduate students in analytic number theory.

Keywords

Congruences Exponential sums Mean value Modular forms Prime Zeta functions number theory

Editors and affiliations

  • Wenpeng Zhang
    • 1
  • Yoshio Tanigawa
    • 2
  1. 1.Northwest UniversityXi’anP.R. China
  2. 2.Nagoya UniversityNagoyaJapan

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-30829-6
  • Copyright Information Springer Science+Business Media, Inc. 2006
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-30414-4
  • Online ISBN 978-0-387-30829-6
  • Series Print ISSN 1389-2177