Displaying similar documents to “Mean-periodicity and zeta functions”

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...

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

Franziska Heinloth (2007)

Annales de l’institut Fourier

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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.

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...

On Witten multiple zeta-functions associated with semisimple Lie algebras I

Kohji Matsumoto, Hirofumi Tsumura (2006)

Annales de l’institut Fourier

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We define Witten multiple zeta-functions associated with semisimple Lie algebras 𝔰𝔩 ( n ) , ( n = 2 , 3 , ... ) of several complex variables, and prove the analytic continuation of them. These can be regarded as several variable generalizations of Witten zeta-functions defined by Zagier. In the case 𝔰𝔩 ( 4 ) , we determine the singularities of this function. Furthermore we prove certain functional relations among this function, the Mordell-Tornheim double zeta-functions and the Riemann zeta-function. Using these relations,...