Laurent series expansions of $L$-functions

Tushar Karmakar; Saikat Maity; Bibekananda Maji

Laurent series expansions of $L$-functions

Number Theory 2024-10-04 v1

Authors: Tushar Karmakar , Saikat Maity , Bibekananda Maji

Abstract

One of the main objectives of the current paper is to revisit the well known Laurent series expansions of the Riemann zeta function $\zeta(s)$ , Hurwitz zeta function $\zeta(s,a)$ and Dirichlet $L$ -function $L(s,\chi)$ at $s=1$ . Moreover, we also present a new Laurent series expansion of $L$ -functions associated to cusp forms over the full modular group.

Keywords

Laurent series Riemann zeta function Hurwitz zeta function Dirichlet L-function cusp forms

Cite

@article{arxiv.2410.02265,
  title  = {Laurent series expansions of $L$-functions},
  author = {Tushar Karmakar and Saikat Maity and Bibekananda Maji},
  journal= {arXiv preprint arXiv:2410.02265},
  year   = {2024}
}

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