On the asymptotics of a cotangent sum related to the Estermann zeta function
Abstract
The sum c0(1/k)=-Σm=1k-1(m/k)(mπ/k) is related to the Estermann zeta function. A recent paper computes the first two terms of the large-k asymptotic expansion of c0(1/k). Using the Poisson summation formula for finite sums, we find three additional terms.
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