Gál-type GCD sums beyond the critical lineBondarenko, 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
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/SummaryWe 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.
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