Displaying similar documents to “On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras”

A mean value theorem for the square of class number times regulator of quadratic extensions

Takashi Taniguchi (2008)

Annales de l’institut Fourier

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Let k be a number field. In this paper, we give a formula for the mean value of the square of class number times regulator for certain families of quadratic extensions of k characterized by finitely many local conditions. We approach this by using the theory of the zeta function associated with the space of pairs of quaternion algebras. We also prove an asymptotic formula of the correlation coefficient for class number times regulator of certain families of quadratic extensions. ...

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.

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...

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,...