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An exponentially-averaged Vasyunin formula. (English) Zbl 07352296
Let \(f_\alpha(t)=\frac{1}{\alpha t}-\frac{1}{e^{\alpha t}-1}\). In the paper under review the authors compute the integral \(\int_0^\infty f_m(t)f_n(t)dt\) for coprime integers \(m,n\geq 1\), where the answer may read as a reciprocity formula for cotangent sums. The work is motivated by studying a probabilistic version of the Nyman-Beurling criterion for the Riemann hypothesis.

MSC:
11L03 Trigonometric and exponential sums (general theory)
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
11F20 Dedekind eta function, Dedekind sums
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References:
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