The Lerch zeta function as a fractional derivative
Complex Variables
2021-05-03 v1 Classical Analysis and ODEs
Number Theory
Abstract
We derive and prove a new formulation of the Lerch zeta function as a fractional derivative of an elementary function. We demonstrate how this formulation interacts very naturally with basic known properties of Lerch zeta, and use the functional equation to obtain a second formulation in terms of fractional derivatives.
Cite
@article{arxiv.1804.07936,
title = {The Lerch zeta function as a fractional derivative},
author = {Arran Fernandez},
journal= {arXiv preprint arXiv:1804.07936},
year = {2021}
}
Comments
10 pages; peer-reviewed and accepted in Banach Center Publications as part of proceedings of Number Theory Week 2017