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