Rabinowitsch revisited
Random matrices, magic squares and matching polynomials.
Rapidly convergent series representations for ζ(2n+1) and their χ-analogue
Real Zeros of Eisenstein Series.
Real zeros of general -functions
In questo lavoro vengono studiati gli zeri reali di una classe di serie di Dirichlet, che generalizzano le funzioni , definite in [8], Combinando le tecniche elementari di Pintz [9] con alcuni metodi analitici si ottiene l’estensione dei classici teoremi di Hecke e Siegel.
Recent progress in the theory of L-functions.
Recent progress in the theory of L-functions
Refinement of an estimate for the Hurwitz zeta function in a neighbourhood of the line σ = 1
The well-known estimate of the order of the Hurwitz zeta function 0. The improvement of the constant c is a consequence of some technical modifications in the method of estimating exponential sums sketched by Heath-Brown ([11], p. 136).
Relations between the values of zeta and L-functions at integral arguments
Relative zeta determinants and the geometry of the determinant line bundle.
Remark on Dirichlet series satisfying functional equations.
Remarks on the LindelÖf Hypothesis
Remarks on the upper bound for L(1,χ)
Remarks on Weil’s quadratic functional in the theory of prime numbers, I
This Memoir studies Weil’s well-known Explicit Formula in the theory of prime numbers and its associated quadratic functional, which is positive semidefinite if and only if the Riemann Hypothesis is true. We prove that this quadratic functional attains its minimum in the unit ball of the -space of functions with support in a given interval , and prove again Yoshida’s theorem that it is positive definite if is sufficiently small. The Fourier transform of the functional gives rise to a quadratic...
Répartition des valeurs d'une somme de fonctions exponentielles
Répartition des zéros des fonctions et matrices aléatoires
Representation growth of linear groups
Let be a group and the number of its -dimensional irreducible complex representations. We define and study the associated representation zeta function . When is an arithmetic group satisfying the congruence subgroup property then has an “Euler factorization”. The “factor at infinity” is sometimes called the “Witten zeta function” counting the rational representations of an algebraic group. For these we determine precisely the abscissa of convergence. The local factor at a finite place...
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...
Repulsive behavior in an exceptional family
Résidu en s = 1 des fonctions zeta p-adiques.