On certain Fourier expansions for the Riemann zeta function
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866914073105399808 |
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| author | Patkowski, Alexander E. |
| author_facet | Patkowski, Alexander E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_12962 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On certain Fourier expansions for the Riemann zeta function Patkowski, Alexander E. Number Theory 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. |
| title | On certain Fourier expansions for the Riemann zeta function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2007.12962 |