二次Waring-Goldbach问题  

The quadratic Waring-Goldbach problem

作　　者：刘建亚[1] 展涛[1] 

机构地区：[1]山东大学数学与系统科学学院,山东济南250100

出　　处：《山东大学学报（理学版）》2007年第2期1-18,共18页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金重点项目(10531060);教育部科学技术重大项目资助(305009)

摘　　要：本文简述二次Waring-Goldbach问题的最新进展,具体内容包括:Waring-Goldbach问题,圆法,具有五个几乎相等变量的华罗庚定理,扩张主区间,四个素数平方之和的主区间,Dirichlet多项式的均值定理,四个素数平方之和的余区间与例外集,素变数三角和的新估计,四个素数平方之和与筛法,殆素数变量的Lagrange定理,Linnik-Gallagher问题,再论具有五个几乎相等变量的华罗庚定理,三个殆素数的平方和,Sarnak猜想与三元二次型.The purpose of this paper is to briefly survey recent progress towards the quadratic Waring-Goldbach problem. Contents of the paper are as follows： the Waring-Goldbach problem, the circle method, Hua＇s theorem with five almost equal prime variables, treatment of the enlarged major arcs, the major arcs in the representation by four squares of primes, mean-value estimates for Diricblet pelynomials, the minor arcs and exceptional set in the representation by four squares of primes, estimates of exponential sums over primes, sieve methods in the representation by four squares of primes, Lagrange＇s theorem with almost prime variables, the Linnik-Gallagher problem, new results for Hua＇ s theorem with five almost equal prime variables, sums of three squares of almost primes, Sarnak＇ s conjecture and ternary quadratic forms.

关 键 词：二次Waring-Goldbach问题 圆法 筛法 自守形式 Jacquet--Langlands对应 Selberg特征值猜想 

分 类 号：O156[理学—数学]