Displaying similar documents to “A note on functional equations for zeta functions with values in Chow motives”

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

Takashi Taniguchi (2007)

Annales de l’institut Fourier

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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...

The monodromy conjecture for zeta functions associated to ideals in dimension two

Lise Van Proeyen, Willem Veys (2010)

Annales de l’institut Fourier

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The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot. However in full generality it is proven only for zeta functions associated to polynomials in two variables. In this article we work with zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A’Campo) to compute the “Verdier monodromy” eigenvalues...

Mean-periodicity and zeta functions

Ivan Fesenko, Guillaume Ricotta, Masatoshi Suzuki (2012)

Annales de l’institut Fourier

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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...