Combinatorial relations for Euler-Zagier sums
Completely q-multiplicative functions: the Mellin transform approach
Complex dimensions of self-similar fractal strings and Diophantine approximation.
Comportement asympotique des hauteurs des points de Heegner
Le terme principal de la moyenne, sur les discriminants quadratiques satisfaisant la condition de Heegner, de la hauteur de Néron-Tate des points de Heegner d’une courbe elliptique rationnelle a été déterminé dans [13]. Les auteurs ont également conjecturé l’expression du terme suivant. Dans cet article, il est démontré que cette expression est correcte et une asymptotique précise, qui sauve une puissance dans le terme d’erreur, est obtenue. Les annulations des coefficients de Fourier de formes...
Computing special values of motivic -functions.
Convexity bounds for L-functions
Counting -groups and nilpotent groups
Cramer functions and Guinand equations
Dedekind sums involving Jacobi modular forms and special values of Barnes zeta functions
In this paper we study three new shifted sums of Apostol-Dedekind-Rademacher type. The first sums are written in terms of Jacobi modular forms, and the second sums in terms of cotangent and the third sums are expressed in terms of special values of the Barnes multiple zeta functions. These sums generalize the classical Dedekind-Rademacher sums. The main aim of this paper is to state and prove the Dedekind reciprocity laws satisfied by these new sums. As an application of our Dedekind reciprocity...
Degeneration of multiple Euler products
Dirichlet polynomial approximations to zeta functions
Dirichlet series associated with polynomials
Dirichlet series induced by the Riemann zeta-function
The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form for in . Among other things, using the Haar measure on for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.
Discrete limit theorems for general Dirichlet series. III
Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given.
Discrete universality of the -functions of elliptic curves.
Discrete Value -- Distribution of L-functions of Elliptic Curves
Distinct zeros of functions in the Selberg class
Distinct zeros of L-functions
Distribution of digits in integers: fractal dimensions and zeta functions
Distribution of values of Hecke characters of infinite order
We show that the number of primes of a number field K of norm at most x, at which the local component of an idele class character of infinite order is principal, is bounded by O(x exp(-c√(log x))) as x → ∞, for some absolute constant c > 0 depending only on K.