Zeta functions over zeros of general zeta and $L$-functions

Details Zeta functions over zeros of general zeta and $L$-functions Zeta functions over zeros of general zeta and $L$-functions

2003-11-04

arxiv.org/abs/math/0311029v1

in book: Zeta Functions, Topology and Quantum Physics, eds. T. Aoki et al., Springer (2005) pp. 171-196

Mathematics

Complex Variables

latex ell.tex, 1 file, 26 pages, 7 tables; in: Proceedings of The International Symposium on Zeta Functions, Topology and Quan

Scientific paper

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.

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