International Symposium in Memory of Hua Loo Keng : Volume I Number Theory

The international symposium on number theory and analysis in memory of the late famous Chinese mathematician Professor Hua Loo Keng took place in August 1988 at the Tsinghua University in Beijing. Excellent survey lectures and expositions of the most recent results in number theory and analysis were given by experts from all over the world. While Volume I focuses on number theory, Volume II deals mainly with several complex variables, differential geometry and classical complex analysis. Both volumes also include two fascinating accounts of Professor Hua Loo Keng's life and work by Professor S. Iyanaga and Professor Wang Yuan. Highlights in Volume I: D.A. Hejhal: Eigenvalues of the Laplacian for PSL (2 Z): Some new Results and Computational Techniques.- A.A. Karatsuba: On the Zeros of Riemann's Zeta-Function on the Critical Line.- H.E. Richert: Aspects of the Small Sieve.- W.M. Schmidt: On the Number of Good Simultaneous Approximations to Algebraic Numbers.- M.V. Subbarao, Wang Yuan: On a Generalized Waring's Problem in Algebraic Number Fields.- G. Wüstholz: From Baker to Mordell. Highlights in Volume II: F. Capocasa, F. Catanese: Periodic Meroporphic Functions and Lefschetz Type Theorems on Quasi-Abelian Varieties.- S.S. Chern:Families of Hypersurfaces Under Contact Transformations in Rn.- G. Dethloff, H. Grauert: On the Infinitesimal Deformation of Simply Connected Domains in One Complex Variable.- D. Drasin: Asymptotic Periods of Entire and Meromorphic Functions.- D. Gaier: On the Convergence of the Bieberbach Polynomials in Regions With Corners.- Gong Sheng, Zheng Xuena: Distortion Theorem for Biholomorphic Mappings in Transitive Domains (I).- C.O. Kiselman: Tangents of Plurisubharmonic Functions.- A. Korányi: Hua-Type Integrals, Hypergeometric Functions and Symmetric Polynomials.- J. Mitchell: Two-Sided L1-Estimates for Szegö Kernels on Classical Domains.- I. Satake: On the Rational Structures of Symmetric Domains, I.- Y.-T. Siu: Some Problems of Rigidity in Several Complex Variables.- S.-T. Yau, F. Zheng: On Projective Manifolds Covered by Space in Cn. Front Matter....Pages i-x Hua Loo Keng: A Brief Outline of his Life and Works....Pages 1-14 Professor Hua Loo Keng in Japan....Pages 15-18 On the Least Prime in an Arithmetical Progression and Theorems Concerning the Zeros of Dirichlet’s L -Functions ( V )....Pages 19-42 Eigenvalues of the Laplacian for PSL (2, Z): Some New Results and Computational Techniques....Pages 43-57 Three Primes Theorem in a Short Interval (II)....Pages 59-102 On the Zeros of Riemann’s Zeta-Function on the Critical Line....Pages 103-115 Small Prime Solutions of a Pair of Linear Equations in Five Variables....Pages 117-162 Hecke Operator and Pellian Equation Conjecture....Pages 163-182 Lower Bound for Number of B-Twins in Short Intervals....Pages 183-191 Legendre Polynomial over Finite Fields and Factorization of Integers....Pages 193-208 Modular Forms of Weight 3/2 Related to Class Numbers....Pages 209-223 On the Congruent Number Problem....Pages 225-229 Aspects of the Small Sieve....Pages 231-234 On the Number of Good Simultaneous Approximations to Algebraic Numbers....Pages 235-248 On a Generalized Waring’s Problem in Algebraic Number Fields....Pages 249-264 Solutions of x + y = z in Numbers Which Are Almost S - Units....Pages 265-277 Fourth Power Mean Value of Dirichlet’s L -Functions....Pages 279-291 From Baker to Mordell....Pages 293-321 On the Arithmetic Properties of G -Functions....Pages 323-330 Uniform Distribution of Values of Multiplicative Functions....Pages 331-346 Back Matter....Pages 347-353 ....Pages 355-356 The international symposium on number theory and analysis in memory of the late famous Chinese mathematician Prof. Hua Loo Keng was co-sponsored by the Institute of Mathematics, Academia Sinica and the University of Science and Technology of China. lt took place between August Ist and 7th of 1988 on the campus of Tsing Hua University, and some 150 mathematicians were pres ent. The symposium was carried out in two separate sections: number theory and analysis. This is retlected in the publication ofa set oftwo volumes, the first one on Number Theory edited by Professor Wang Yuan and the second on Analysis by Professors Gong Sheng, Lu Qi-keng and Yang Lo. The distinguished list of main speakers and the contents of these two vol umes reflect the high level of the mathematical activity throughout the seven days. W e pay special tribute to our main speakers professors Chuang, Conn, Ding, Drasin, Fitzgerald, Gaier, Gong, Grauert, Gu, Hejhal, Iyanaga, Karatsuba, Koranyi, Liao, Lu, Pan, Richert, Satake, Schmidt, Siu, Tatuzawa, Tsang, Vladimirov, Y. Wang, G.Y. Wang, Wüstholz and Yang, who gave the excellent one hour lectures, and also to the participants who gave contributed talks on their own research work. The discussions among the mathematicians were always in a warm atmosphere. Our thanks go to professors Chern, Subbarao and Yau for their contributions to these proceedings