Let fk(n) be the characteristic function of n with Ω(n) = k, and T k(x,α)=∑n≤xfk(n)e(nα).The main purpose of this paper is to establish a Bombieri-type mean-value theorem for Tk(x, α), via using the ...Let fk(n) be the characteristic function of n with Ω(n) = k, and T k(x,α)=∑n≤xfk(n)e(nα).The main purpose of this paper is to establish a Bombieri-type mean-value theorem for Tk(x, α), via using the modified Huxley-Hooley contour and the large-sieve type zero-density estimate for Dirichlet L-functions. The result plays an important role in handling the enlarge major arcs when we try to solve the Waring-Goldbach type problem by the circle method展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11271249)the First-class Discipline of Universities in Shanghai
文摘Let fk(n) be the characteristic function of n with Ω(n) = k, and T k(x,α)=∑n≤xfk(n)e(nα).The main purpose of this paper is to establish a Bombieri-type mean-value theorem for Tk(x, α), via using the modified Huxley-Hooley contour and the large-sieve type zero-density estimate for Dirichlet L-functions. The result plays an important role in handling the enlarge major arcs when we try to solve the Waring-Goldbach type problem by the circle method