**Contemporary Mathematics**

Volume: 77;
1988;
170 pp;
Softcover

MSC: Primary 11;

**Print ISBN: 978-0-8218-5084-8
Product Code: CONM/77**

List Price: $34.00

AMS Member Price: $27.20

MAA Member Price: $30.60

**Electronic ISBN: 978-0-8218-7665-7
Product Code: CONM/77.E**

List Price: $32.00

AMS Member Price: $25.60

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# Number Theory and Its Applications in China

Share this page *Edited by *
*Wang Yuan; Yang Chung-chun; Pan Cheng-biao*

Of all modern mathematical forms, number theory is one of the
earliest to be explored in China and is the one to which the Chinese have made
their greatest contributions. Yan Wu-zhi first introduced number theory into
China in the 1920s. Particularly influential in the field was Hua Loo-keng,
who studied with G. H. Hardy and made significant contributions in the areas
estimating complete exponential sums, Waring's problems, Tarry's problems, and
Vinogradov's method. Interest in number theory continued to flourish following
the founding of the People's Republic of China. The most noted accomplishments
by Chinese mathematicians were focused on the solution of Goldbach's
Conjecture and on the sieve method. Although the Cultural Revolution
interrupted research in number theory for more than 10 years, the field is now
growing in China. A number of universities now have advanced programs in the
subject and a wide variety of topics, including the applications of number
theory.

This volume contains nine survey articles and three articles on current
research. The collection emphasizes the accomplishments of Chinese number
theorists during 1949-1979, a period when correspondence between China and
other countries was discouraged. The collection is intended not only to survey
the significant contributions of Chinese mathematicians, but also to reflect
the latest developments and current state of research in number theory in
China.

# Table of Contents

## Number Theory and Its Applications in China

- Contents ix10 free
- Preface xi12 free
- Contributors xiii14 free
- Analytic Number Theory in China I 116 free
- Analytic Number Theory in China II 1934
- Number Theoretic Method in Numerical Analysis 6378
- Diophantine Equations and Diophantine Inequalities in Algebraic Number Fields 8398
- Some Results of Modular Forms 95110
- Some Results in the Application of the Number theory to Digital Signal Processing and Public-Key Systems 107122
- Some Results on Diophantine Equations 113128
- Diophantine Approximation and Transcendental Number Theory 127142
- Quadratic Forms and Hermtian Forms 143158
- Small Prime Solutions of Linear Equations and the Exceptional Set in Goldbach's Problem 153168
- On the Relative Trace Formula 159174
- Kloosterman Integrals and Base Change 163178