On certain Fourier expansions for the Riemann zeta function

2020/07/25 by Patkowski, Alexander E.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2007.12962

Abstract

We build on a recent paper on Fourier expansions for the Riemann zeta function. We establish Fourier expansions for certain L-functions, and offer series representations involving the Whittaker function W_γ,μ(z) for the coefficients. Fourier expansions for the reciprocal of the Riemann zeta function are also stated. A new expansion for the Riemann xi function is presented in the third section by constructing an integral formula using Mellin transforms for its Fourier coefficients.

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