Displaying similar documents to “The monodromy conjecture for zeta functions associated to ideals in dimension two”

A note on functional equations for zeta functions with values in Chow motives

Franziska Heinloth (2007)

Annales de l’institut Fourier

Similarity:

We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the λ –structure of this ring, we deduce a functional equation for the zeta function of abelian varieties. Furthermore, we show that the property of having a rational zeta function satisfying a functional equation is preserved under products.

On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras

Takashi Taniguchi (2007)

Annales de l’institut Fourier

Similarity:

In this paper we consider the prehomogeneous vector space for a pair of simple algebras which are inner forms of the D 4 type and the E 6 type. We mainly study the non-split cases. The main purpose of this paper is to determine the principal parts of the global zeta functions associated with these spaces when the simple algebras are non-split. We also give a description of the sets of rational orbits of these spaces, which clarifies the expected density theorems arising from the properties...

Mean-periodicity and zeta functions

Ivan Fesenko, Guillaume Ricotta, Masatoshi Suzuki (2012)

Annales de l’institut Fourier

Similarity:

This paper establishes new bridges between zeta functions in number theory and modern harmonic analysis, namely between the class of complex functions, which contains the zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of an arithmetic scheme with its expected analytic shape...