Zeta functions over zeros of general zeta and $L$-functions
Complex Variables
2007-05-23 v1 Number Theory
Abstract
We describe in detail three distinct families of generalized zeta functions built over the (nontrivial) zeros of a rather general arithmetic zeta or L-function, extending the scope of two earlier works that treated the Riemann zeros only. Explicit properties are also displayed more clearly than before. Several tables of formulae cover the simplest concrete cases: L-functions for real primitive Dirichlet characters, and Dedekind zeta functions.
Cite
@article{arxiv.math/0311029,
title = {Zeta functions over zeros of general zeta and $L$-functions},
author = {A. Voros},
journal= {arXiv preprint arXiv:math/0311029},
year = {2007}
}
Comments
latex ell.tex, 1 file, 26 pages, 7 tables; in: Proceedings of The International Symposium on Zeta Functions, Topology and Quantum Physics (ZTQ 2003) Osaka, Japan March 3-6 2003