## Abstract

This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators {Tm:m≥1} given by Tm(f)(a,c)=1m∑k=0m-1f(a+km,mc) acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter values. The actions of various related operators on these function spaces are determined. It is shown that, for each s∈ C, there is a two-dimensional vector space spanned by linear combinations of Lerch zeta functions characterized as a maximal space of simultaneous eigenfunctions for this family of Hecke operators. This is an analog of a result of Milnor for the Hurwitz zeta function. We also relate these functions to a linear partial differential operator in the (a, c)-variables having the Lerch zeta function as an eigenfunction.

Original language | English (US) |
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Article number | 33 |

Journal | Research in Mathematical Sciences |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2016 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Mathematics (miscellaneous)
- Computational Mathematics
- Applied Mathematics