An exponentially-averaged Vasyunin formula

Darses, Sébastien; Hillion, Erwan

doi:10.1090/proc/15422

An exponentially-averaged Vasyunin formula
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by Sébastien Darses and Erwan Hillion PDF

Proc. Amer. Math. Soc. 149 (2021), 2969-2982 Request permission

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 by Bettin and Conrey [Int. Math. Res. Not. IMRN 24 (2013), pp. 5709–5726] and Auli, Bayad, and Beck [Acta Arith. 181 (2017), pp. 297–319].

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