On character sums of binary quadratic forms

JOURNAL OF NUMBER THEORY

卷:129

Article

Chang, Mei-Chu

关键词: Character sums;    Quadratic residues;    Burgess;   

DOI  :  10.1016/j.jnt.2009.02.017

来源: Elsevier

【 摘 要 】

We establish character sum bounds of the form vertical bar Sigma (a <= x <= a+H) (b <= y <= b+H) chi(x(2) + ky(2))vertical bar < p(-tau) H-2, where chi is a non-trivial character (mod p), p(1/4+epsilon) < H < p, and vertical bar a vertical bar, vertical bar b vertical bar < p(epsilon/2)H. As an application, we obtain that given k is an element of Z\{0}, x(2) + k is a quadratic non-residue (mod p) for some 1 <= x < p(1/2 root e+is an element of). (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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