Laurent series expansions of $L$-functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909334100770816 |
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| author | Karmakar, Tushar Maity, Saikat Maji, Bibekananda |
| author_facet | Karmakar, Tushar Maity, Saikat Maji, Bibekananda |
| contents | One of the main objectives of the current paper is to revisit the well known Laurent series expansions of the Riemann zeta function $ζ(s)$, Hurwitz zeta function $ζ(s,a)$ and Dirichlet $L$-function $L(s,χ)$ at $s=1$. Moreover, we also present a new Laurent series expansion of $L$-functions associated to cusp forms over the full modular group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Laurent series expansions of $L$-functions Karmakar, Tushar Maity, Saikat Maji, Bibekananda Number Theory Primary 11M06, Secondary 11M41 One of the main objectives of the current paper is to revisit the well known Laurent series expansions of the Riemann zeta function $ζ(s)$, Hurwitz zeta function $ζ(s,a)$ and Dirichlet $L$-function $L(s,χ)$ at $s=1$. Moreover, we also present a new Laurent series expansion of $L$-functions associated to cusp forms over the full modular group. |
| title | Laurent series expansions of $L$-functions |
| topic | Number Theory Primary 11M06, Secondary 11M41 |
| url | https://arxiv.org/abs/2410.02265 |