On certain Fourier expansions for the Riemann zeta function

25 Jul 2020  ·  Patkowski Alexander E ·

We build on a recent paper on Fourier expansions for the Riemann zeta function. It is shown that a new criteria for the Riemann Hypothesis follows from a theorem of Wiener... We establish Fourier expansions for certain $L$-functions, and offer series representations involving the Whittaker function $W_{\gamma,\mu}(z)$ for the coefficients. 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. read more

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Number Theory