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Article Dans Une Revue Mathematical Methods in the Applied Sciences Année : 2018

Reciprocity formulae for generalized Dedekind‐Vasyunin‐cotangent sums

Résumé

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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Dates et versions

hal-04463429 , version 1 (17-02-2024)

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Abdelmejid Bayad, Mouloud Goubi. Reciprocity formulae for generalized Dedekind‐Vasyunin‐cotangent sums. Mathematical Methods in the Applied Sciences, 2018, 42 (4), pp.1082-1098. ⟨10.1002/mma.5414⟩. ⟨hal-04463429⟩
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