Functional equation of zeta functions in several variables associated with homogeneous cones

Date/heure
31 janvier 2019
14:15 - 15:15

Oratrice ou orateur
Hideto Nakashima

Catégorie d'évènement
Séminaire Théorie de Lie, Géométrie et Analyse


Résumé

In the study of the Riemann zeta function, a functional equation plays a fundamental role, and it has been confirmed in many mathematical areas that several kinds of zeta functions satisfy functional equations. In 1961, M. Sato found out that there are big group actions behind such functional equations, and then he reached the notion of prehomogeneous vector spaces. In this talk, I focus on solvable prehomogeneous vector spaces associated with homogeneous cones and consider the associated zeta functions in several variables. In particular, an explicit formula of functional equations of these zeta functions is given.