English

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

Classical Analysis and ODEs 2018-07-24 v1

Abstract

The sum c0(1/k)=m=1k1(m/k)cot(mπ/k)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-kk asymptotic expansion of c0(1/k)c_0(1/k). Using the Poisson summation formula for finite sums, we find three additional terms.

Keywords

Cite

@article{arxiv.1807.08527,
  title  = {On the asymptotics of a cotangent sum related to the Estermann zeta function},
  author = {George Fikioris},
  journal= {arXiv preprint arXiv:1807.08527},
  year   = {2018}
}