On the number of representations of integers by quadratic forms in twelve variables.
On the number of representations of positive integers by quadratic forms as the basis of the space .
On the Poles of Andranov L-Functions.
On the representation of numbers by the direct sums of some quaternary quadratic forms.
On the representation of the integer by positive quadratic forms with square-free variables
On the Shintani zeta function for the space of binary quadratic forms.
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 Weil-Siegel formula.
On the Weil-Siegel formula II.
On theta series vanishing at ∞ and related lattices
Primitive lattice points inside an ellipse
Let be a positive definite binary quadratic form with arbitrary real coefficients. For large real , one may ask for the number of primitive lattice points (integer points with ) in the ellipse disc , in particular, for the remainder term in the asymptotics for . While upper bounds for depend on zero-free regions of the zeta-function, and thus, in most published results, on the Riemann Hypothesis, the present paper deals with a lower estimate. It is proved that the absolute value or...
Quotients of Theta Series as Rational Functions of J and ?.
Rationality of a certain formal power series attached to local densities of quadratic forms.
Real Zeros of Eisenstein Series.
Représentations des algèbres de rang 2 et fonctions zêta associées
Dans un travail précédent nous avons défini et étudié la fonction zêta associée à une représentation d’une algèbre de Jordan euclidienne déployée et à un réseau dans l’espace de la représentation. Nous avons démontré la convergence dans un demi-plan, établi l’existence d’un prolongement méromorphe et d’une équation fonctionnelle scalaire. Cette fonction est une généralisation de la fonction zêta de Koecher; elle est donnée dans son domaine de convergence, par une série qui somme sur certains éléments...
Séries thêta des formes quadratiques indéfinies
Special values of multiple gamma functions
We give a Chowla-Selberg type formula that connects a generalization of the eta-function to with multiple gamma functions. We also present some simple infinite product identities for certain special values of the multiple gamma function.
Sums of nine squares
The Adelic Zeta Function Associated to the Space of Binary Cubis Forms. Part I: Global Theory.
The adelic zeta function associated to the space of binary cubic forms. II: Local theory.