NYJM Logo

New York Journal of Mathematics
Volume 31 (2025), 1381-1392

  

Alexander E. Patkowski

On certain Fourier expansions for the Riemann zeta function

view    print


Published: October 3, 2025.
Keywords: Riemann zeta function; Riemann Hypothesis; Fourier series.
Subject [2010]: 11L20, 11M06.

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 Wγ,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.

Acknowledgements

N/A


Author information

Alexander E. Patkowski
1390 Bumps River Rd.
Centerville, MA 02632, USA

alexepatkowski@gmail.com