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Number Theory

Tradition and Modernization

  • Conference proceedings
  • © 2006

Overview

Editors:
  1. Wenpeng Zhang

    1. Northwest University, Xi’an, P.R. China

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  2. Yoshio Tanigawa

    1. Nagoya University, Nagoya, Japan

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    You can also search for this editor in PubMed   Google Scholar

  • Deals with various aspects of number theory, with some chapters taking an algorithmic point of view and
  • some taking a historical perspective
  • Includes supplementary material: sn.pub/extras

Part of the book series: Developments in Mathematics (DEVM, volume 15)

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Table of contents (16 papers)

  1. Front Matter

    Pages i-xiii
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  2. Positive Finiteness of Number Systems

    • Shigeki Akiyama
    Pages 1-10

  3. On a Distribution Property of the Residual Order of a (mod p)— IV

    • Koji Chinen, Leo Murata
    Pages 11-22

  4. Diagonalizing “Bad” Hecke Operators on Spaces of Cusp Forms

    • YoungJu Choie, Winfried Kohnen
    Pages 23-26

  5. On the Hilbert-Kamke and the Vinogradov Problems in Additive Number Theory

    • Vladimir N. Chubarikov
    Pages 27-37

  6. The Goldbach-Vinogradov Theorem in Arithmetic Progressions

    • Zhen Cui
    Pages 39-65

  7. Densities of Sets of Primes Related to Decimal Expansion of Rational Numbers

    • Toshihiro Hadano, Yoshiyuki Kitaoka, Tomio Kubota, Michihiro Nozaki
    Pages 67-80

  8. Spherical Functions on p-Adic Homogeneous Spaces

    • Yumiko Hironaka
    Pages 81-95

  9. On Modular forms of Weight (6n + 1)/5 Satisfying a Certain Differential Equation

    • Masanobu Kaneko
    Pages 97-102

  10. Some Aspects of the Modular Relation

    • Shigeru Kanemitsu, Yoshio Tanigawa, Haruo Tsukada, Masami Yoshimoto
    Pages 103-118

  11. Zeros of Automorphic L-Functions and Noncyclic Base Change

    • Jianya Liu, Yangbo Ye
    Pages 119-152

  12. Analytic Properties of Multiple Zeta-Functions in Several Variables

    • Kohji Matsumoto
    Pages 153-173

  13. Cubic Fields and Mordell Curves

    • Katsuya Miyake
    Pages 175-183

  14. Towards the Reciprocity of Quartic Theta-Weyl Sums, and Beyond

    • Yoshinobu Nakai
    Pages 185-204

  15. Explicit Congruences for Euler Polynomials

    • Zhi-Wei Sun
    Pages 205-218

  16. Square-Free Integers as Sums of Two Squares

    • Wenguang Zhai
    Pages 219-227

  17. Some Applications of L-Functions to the Mean Value of the Dedekind Sums and Cochrane Sums

    • Zhang Wenpeng
    Pages 229-237

  18. Back Matter

    Pages 239-241
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Keywords

About this book

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.

Editors and Affiliations

  • Northwest University, Xi’an, P.R. China

    Wenpeng Zhang

  • Nagoya University, Nagoya, Japan

    Yoshio Tanigawa

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