# Number Theory

## Tradition and Modernization

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

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

**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.

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

- 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
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