An exponentially averaged Vasyunin formula

Abstract

We prove a Vasyunin-type formula for an autocorrelation function arising from a Nyman-Beurling criterion generalized to a probabilistic framework. This formula can also be seen as a reciprocity formula for cotangent sums, related to the ones proven in [BC13], [ABB17].

This paper has been written from results already stated in a previous version of another paper in 2018, but has been now submitted separately. arXiv admin note: text overlap with arXiv:1805.06733