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arXiv · 1807.08527

On the asymptotics of a cotangent sum related to the Estermann zeta function

George Fikioris
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Abstract

The sum $c_0(1/k)=-\sum_{m=1}^{k-1}(m/k)\cot(m{\pi}/k)$ is related to the Estermann zeta function. A recent paper computes the first two terms of the large-$k$ asymptotic expansion of $c_0(1/k)$. Using the Poisson summation formula for finite sums, we find three additional terms.

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George Fikioris. 2018-07-23. On the asymptotics of a cotangent sum related to the Estermann zeta function. https://arxiv.org/abs/1807.08527

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