二次Waring-Goldbach问题

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 quadratic Waring-Goldbach problem

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 Dirichlet polynomials,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.