On the representation of H-invariants in the Selberg class
On the Shintani zeta function for the space of binary quadratic forms.
On the singularities of multiple L-functions
We investigate the singularities of a class of multiple L-functions considered by Akiyama and Ishikawa [2].
On the structure of the Selberg class, IV: basic invariants
On the structure of the Selberg class, VI: non-linear twists
On the value-distribution of Epstein zeta-functions.
We investigate the value-distribution of Epstein zeta-functions ζ(s; Q), where Q is a positive definite quadratic form in n variables. We prove an asymptotic formula for the number of c-values, i.e., the roots of the equation ζ(s; Q) = c, where c is any fixed complex number. Moreover, we show that, in general, these c-values are asymmetrically distributed with respect to the critical line Re s =n/4. This complements previous results on the zero-distribution.[Proceedings of the Primeras Jornadas...
On the Zeros of a Class of Generalised Dirichlet Series-XVI.
On the zeros of degree one L-functions from the extended Selberg class
On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras
In this paper we consider the prehomogeneous vector space for a pair of simple algebras which are inner forms of the type and the 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 of these...
On Tornheim's double series
On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions
On Witten multiple zeta-functions associated with semisimple Lie algebras I
We define Witten multiple zeta-functions associated with semisimple Lie algebras , 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 , 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, we prove...
On zeros of approximate functions of the Rankin-Selberg L-functions
On zeta-functions associated to certain cusp forms. I
In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained.
On zeta-functions associated to certain cusp forms. II
A formula for the mean value of multiplicative functions associated to certain cusp forms is obtained. The paper is a continuation of [4].
Ordre, convergence et sommabilité de produits de séries de Dirichlet
L’article donne des réponses optimales ou presque optimales aux questions suivantes, qui remontent à Stieltjes, Landau et Bohr, et concernent des séries de Dirichlet
Petits zéros de fonctions L de formes modulaires
Positively finitely generated groups.
Primitive lattice points in convex planar domains
Prolongements analytiques d’une classe de fonctions zêta des hauteurs et applications
Nous montrons dans la première partie l’existence d’un prolongement méromorphe à tout le plan complexe et explicitons les propriétés et quelques conséquences, d’une large classe de séries zêta des hauteurs associées à l’espace projectif