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Number Theory and Its Applications in China
Edited by: Wang Yuan, Yang Chung-chun, and Pan Cheng-biao
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Contemporary Mathematics
1988; 170 pp; softcover
Volume: 77
ISBN-10: 0-8218-5084-9
ISBN-13: 978-0-8218-5084-8
List Price: US$30
Member Price: US$24
Order Code: CONM/77
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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

  • C. Jingrun and P. Chengbiao -- Analytic number theory in China I
  • P. Chengdong, P. Chengbiao, and X. Shenggang -- Analytic number theory in China II
  • W. Yuan -- Number theoretic method in numerical analysis
  • W. Yuan -- Diophantine equations and Diophantine inequalities in algebraic number fields
  • P. Dingyi and F. Xuning -- Some results of modular forms
  • S. Qi -- Some results in the application of the number theory to digital signal processing and public-key systems
  • S. Qi -- Some results on Diophantine equations
  • X. Guangshan -- Diophantine approximation and transcendental number theory
  • L. Delang and L. Hongwen -- Quadratic forms and Hermitian forms
  • L. Mingchit and T. Kaiman -- Small prime solutions of linear equations and the exceptional set in Goldbach's problem
  • K. F. Lai -- On the relative trace formula
  • Y. Yangbo -- Kloosterman integrals and base change
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