Local zeta functions and Meuser's invariant functions

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

Igusa’s Local Zeta Functions of Semiquasihomogeneous Polynomials

In this paper, we prove the rationality of Igusa’s local zeta functions of semiquasihomogeneous polynomials with coefficients in a non-archimedean local field K. The proof of this result is based on Igusa’s stationary phase formula and some ideas on Néron π-desingularization.

On Simple Igusa Local Zeta Functions

The objective of this announcement is the statement of some recent results on the classiication of generalized Igusa local zeta functions associated to irreducible matrix groups. The deenition of a simple Igusa local zeta function will motivate a complete classiication of certain generalized Igusa local zeta functions associated to simply connected simple Chevalley groups. In addition to the no...

Holomorphy of Local Zeta Functions for Curves

Zeta Functions

We review various periodic orbit formulae for the zeta function whose zeros represent semiclassical approximations to the energy levels of chaotic systems. In particular, we focus on the Riemann-Siegel-resummed expression. The emphasis is on the ability of such formulae to reproduce the analytic properties of the spetral determinant, whose zeros are the exact quantum levels. As an example, the ...