Gal-type GCD sums beyond the critical line

JOURNAL OF NUMBER THEORY

卷:166

Article

Bondarenko, Andriy^1,2  Hilberdink, Titus³  Seip, Kristian² 

[1] Taras Shevchenko Natl Univ Kyiv, Dept Math Anal, Volodymyrska 64, UA-01033 Kiev, Ukraine

[2] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

[3] Univ Reading, Dept Math & Stat, Reading RG6 2AH, Berks, England

关键词: Gal's theorem;    GCD sums;    Critical line;   

DOI  :  10.1016/j.jnt.2016.02.017

来源: Elsevier

【 摘 要 】

We prove that [GRAPHICS] holds for arbitrary integers 1 <= n(1) < ... < n(N) and 0 < alpha < 1/2 and show by an example that this bound is optimal, up to the precise value of the exponent b(alpha), This estimate complements recent results for 1/2 <= alpha <= 1 and shows that there is no trace of the functional equation for the Riemann zeta function in estimates for such GCD sums when 0 < alpha < 1/2. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free