Accessibility navigation


Gál-type GCD sums beyond the critical line

Bondarenko, A., Hilberdink, T. and Seip, K. (2016) Gál-type GCD sums beyond the critical line. Journal of Number Theory, 166. pp. 93-104. ISSN 0022-314X

[img]
Preview
Text - Accepted Version
· Available under License Creative Commons Attribution Non-commercial No Derivatives.
· Please see our End User Agreement before downloading.

159kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1016/j.jnt.2016.02.017

Abstract/Summary

We prove that ∑k,ℓ=1N(nk,nℓ)2α(nknℓ)α≪N2−2α(logN)b(α) holds for arbitrary integers 1≤n1<⋯<nN1≤n1<⋯<nN and 0<α<1/20<α<1/2 and show by an example that this bound is optimal, up to the precise value of the exponent b(α)b(α). This estimate complements recent results for 1/2≤α≤11/2≤α≤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<α<1/20<α<1/2.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:63245
Publisher:Elsevier

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation