English

Hurwitz Zeta Functions and Ramanujan's Identity for Odd Zeta Values

Number Theory 2022-05-18 v1

Abstract

Inspired by a famous formula of Ramanujan for odd zeta values, we prove an analogous formula involving the Hurwitz zeta function. We introduce a new integral kernel related to the Hurwitz zeta function, generalizing the integral kernel associated to Ramanujan's identity. We also derive several infinite families of identities analogous to Ramanujan's formula.

Keywords

Cite

@article{arxiv.2205.08183,
  title  = {Hurwitz Zeta Functions and Ramanujan's Identity for Odd Zeta Values},
  author = {Parth Chavan},
  journal= {arXiv preprint arXiv:2205.08183},
  year   = {2022}
}