A generalization of Rademacher's reciprocity law
Volume 159 / 2013
Acta Arithmetica 159 (2013), 363-374
MSC: Primary 11F20; Secondary 11M41.
DOI: 10.4064/aa159-4-5
Abstract
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.
