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Alexander E. Patkowski
On certain Fourier expansions for the Riemann zeta function
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Published: |
October 3, 2025. |
Keywords: |
Riemann zeta function; Riemann Hypothesis; Fourier series. |
Subject [2010]: |
11L20, 11M06. |
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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.
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Acknowledgements
N/A
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Author information
Alexander E. Patkowski
1390 Bumps River Rd.
Centerville, MA 02632, USA
alexepatkowski@gmail.com
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