Number theory, Physics and Geometry, Les Houches, March 2003

A Voros
Zeta functions for the Riemann zeros

Abstract:

A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structure, plus countably many special values) are explicitly displayed.

Some useful reference works:

P. Cartier, An Introduction to Zeta Functions, in: From Number Theory to Physics, M. Wadschmidt, P. Moussa, J.-M. Luck and C. Itzykson eds., Springer-Verlag (1992) 1--63.
H. Davenport, Multiplicative Number Theory (3rd ed., revised by H.L. Montgomery), Graduate Texts in Mathematics 74, Springer-Verlag (2000)
H.M. Edwards, Riemann's Zeta Function, Academic Press (1974)
E.C. Titchmarsh, The Theory of the Riemann Zeta-function (2nd ed., revised by D.R. Heath-Brown), Oxford Univ. Press (1986).

A Voros Zeta functions for the Riemann zeros

Abstract:

lecture:

A Voros
Zeta functions for the Riemann zeros