where $urn:x-wiley:mma:media:mma5414:mma5414-math-0002$ and q are positive coprime integers, and ζ(a,x) denotes the Hurwitz zeta function. We prove explicit formula for the symmetric sum

$urn:x-wiley:mma:media:mma5414:mma5414-math-0003$

which is a new reciprocity law for the sum $urn:x-wiley:mma:media:mma5414:mma5414-math-0004$ . Our result is a complement to recent results dealing with the sum

$urn:x-wiley:mma:media:mma5414:mma5414-math-0005$

studied by Bettin-Conrey and then by Auli-Bayad-Beck. Accidentally, when a = 0, our reciprocity formula improves the known result in a previous study.

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Volume42, Issue4

15 March 2019

Pages 1082-1098

Reciprocity formulae for generalized Dedekind-Vasyunin-cotangent sums

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Reciprocity formulae for generalized Dedekind-Vasyunin-cotangent sums

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