s个几乎相等的素数的k次方和(Ⅱ)

On the sums of a almost equal k-th powers of primes(Ⅱ)

假定 pθ‖ k,当 p =2 ,2 |k时 ,γ =θ +2 ;其他情况时 ,γ =θ +1。而 R = ( p-1) | kpγ。在GRH(广义 Riemann假设 )下 ,证明了当 s≥ 2 k2 (2 logk +log logk +2 .5 ) ,k >1 1时 ,任何足够大的整数 N≡ s(mod R)都可以表示为 s个几乎相等的素数的 k次方和。

Let P θ‖k,γ=θ+2, for P=2,2|k;γ=θ+1,for other p.Then for R=(p-1)|k pγ,it is proved that every suffiently large integer N≡s( mod R) is a sum of s almost equal k th powers of primes subject to the generalized Riemann hypothesis (GRH),where s≥2k 2(2 log k+ log log k+2.5),k>11.