Asymptotic formulas for Vasyunin cotangent sums

Konstantinos A. Draziotis and George Fikioris

Applied Mathematics and Computation, 2020, vol. 383, issue C

Abstract: We study the Vasyunin-type cotangent sum c0(h/k)=−∑m=1k−1(m/k)cot(πhm/k), where h and k are positive coprime integers. This sum is related to Estermann zeta function. By applying the Euler-Maclaurin summation formula to a suitable function, we improve a previous large-k asymptotic approximation of c0(h/k). We also provide a procedure to compute an arbitrary number of terms of the approximation.

Keywords: Vasyunin cotangent sums; Euler-Maclaurin summation formula; Digamma function (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:383:y:2020:i:c:s0096300320303441

DOI: 10.1016/j.amc.2020.125380

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