Elsevier

Journal of Number Theory

Volume 166, September 2016, Pages 93-104
Journal of Number Theory

Gál-type GCD sums beyond the critical line

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Abstract

We prove thatk,=1N(nk,n)2α(nkn)αN22α(logN)b(α) holds for arbitrary integers 1n1<<nN and 0<α<1/2 and show by an example that this bound is optimal, up to the precise value of the exponent b(α). This estimate complements recent results for 1/2α1 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<1/2.

MSC

11C20

Keywords

Gál's theorem
GCD sums
Critical line

Cited by (0)

Bondarenko and Seip were supported by Grant 227768 of the Research Council of Norway.