De nouveaux curieux produits infinis
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
Density estimates for the zeros of L-functions
Die Primfaktorzerlegung der Werte der Kreisteilungspolynome.
Die Primfaktorzerlegung der Werte der Kreisteilungsprobleme. II.
Die Riemannsche Zetafunktion.
Die Weilsche "Explizite Formel" und temperierte Distributionen.
Difference independence of the Riemann zeta function
Differences between consecutive primes
Digit derivatives and application to zeta measures
Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems
We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide...
Dirichlet polynomial approximations to zeta functions
Dirichlet polynomials
Dirichlet Series and Gamma Function Associated with Rational Functions
We investigate zeta regularized products of rational functions. As an application, we obtain the asymptotic expansion of the Euler Gamma function associated with a rational function.
Dirichlet series associated with polynomials
Dirichlet Series Corresponding to Siegel's Modular Forms.
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.
Dirichlet series with functional equations and related arithmetical identities
Dirichlet summations and products over primes.