Dirichlet Series Under Standard Convolutions: Variations on Ramanujan's Identity for Odd Zeta Values
Number Theory
2022-02-04 v3
Abstract
Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its specialization produces new identities and recovers several identities derived earlier in the literature, such as the convolution of squares of Bernoulli numbers by A. Dixit and collaborators, or the convolution of Bernoulli numbers by Y. Komori and collaborators.
Cite
@article{arxiv.2107.06457,
title = {Dirichlet Series Under Standard Convolutions: Variations on Ramanujan's Identity for Odd Zeta Values},
author = {Parth Chavan and Sarth Chavan and Christophe Vignat and Tanay Wakhare},
journal= {arXiv preprint arXiv:2107.06457},
year = {2022}
}
Comments
30 pages