Number Theory Tradition and Modernization [Paperback]

This book collects survey and research papers on various topics in number theory. Although the topics and descriptive details appear varied, they are unified by two underlying principles: first, readability, and second, a smooth transition from traditional approaches to modern ones. Thus, on one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated.

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.

Preface About the book and the conference List of participants Positive finiteness of number systems (S. Akiyama) On a distribution property of the resudual order of a (mod p) IV (K. Chinen and L. Murata) Diagonalizing 'bad Hecke operators on spaces of cusp forms (Y.-J. Choie and W. Kohnen) On the Hilbert-Kamke and the Vinogradov problems in additive number theory (V. N. Chubarikov) The Goldbach-Vinogradov theorem in arithmetic progressions (Z. Cui) Densities of sets of primes related to decimal expansion of rational numbl³A