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 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
URI	https://reading-clone.eprints-hosting.org/id/eprint/63245
Identification Number/DOI	10.1016/j.jnt.2016.02.017
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
Download/View statistics	View download statistics for this item