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A generalization of Rademacher's reciprocity law

Volume 159 / 2013

Sandro Bettin Acta Arithmetica 159 (2013), 363-374 MSC: Primary 11F20; Secondary 11M41. DOI: 10.4064/aa159-4-5


We generalize Rademacher's reciprocity formula for the Dedekind sum to a family of cotangent sums. One of the sums in this family is strictly related to the Vasyunin sum, a function defined on the rationals that is relevant to the Nyman–Beurling–Báez-Duarte approach to the Riemann hypothesis.


  • Sandro BettinSchool of Mathematics
    University of Bristol
    Queens Ave.
    Bristol, BS8 1SN, UK
    Current address:
    Centre de Recherches Mathématiques—Université de Montréal
    P.O. Box 6128, Centre-ville Station
    Montréal, Québec, H3C 3J7, Canada

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