A Bombieri-type Theorem for Exponential Sums  

作　　者：Wei Li YAO 

机构地区：[1]Department of Mathematics,College of Sciences,Shanghai University [2]School of Mathematics,Shandong University

出　　处：《Acta Mathematica Sinica,English Series》2013年第10期1997-2012,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11271249);the First-class Discipline of Universities in Shanghai

摘　　要：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 methodLet 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

关 键 词：Zero-density estimate Huxley-Hooley contour .Bombieri-type theorem 

分 类 号：O174[理学—数学]