Abstract
Recently, several works are done on the generalized Dedekind‐Vasyunin sum urn:x-wiley:mma:media:mma5414:mma5414-math-0001 where 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 . 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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