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Thursday, December 4, 2014

**Abstract:** In a recent paper, Bettin and Conrey define a family of cotangent sums that generalize the classical notion of Dedekind sum and share with it the property of satisfying a reciprocity law. These sums are naturally linked to the computation of estimates of weighted moments of the Riemann zeta function, which are relevant in the approach of Nyman, Beurling, Baez-Duarte and Vasyunin to the Riemann hypothesis. We study particular instances of these arithmetic sums for which it is possible to obtain a simpler reciprocity using an analytic technique introduced by Rademacher in one of several proofs he gave of the reciprocity law of Dedekind sums.