An orthogonal test of the L-functions Ratios Conjecture, II
Artin's conjecture in algebraic number fields and a related question concerning units
Artin's conjecture, Turing's method, and the Riemann hypothesis.
Aspectos computacionales de los números primos (I).
Bounds for automorphic L-functions.
Correction to: "On a positivity property of the Riemann ξ-function" (Acta Arith. 89 (1999), 217-234)
Cramer functions and Guinand equations
Distinct zeros of L-functions
Distribution of zeros of Dirichlet L-functions and an explicit formula for ψ(t,χ)
Distribution of zeros of Dirichlet L-functions and the least prime in an arithmetic progression
Elementary Deuring-Heilbronn phenomenon
Étude d'un problème de continuité lié à l'hypothèse de Riemann
Cet article est consacré à l’étude d’un problème lié au critère de Beurling Nyman sur l’hypothèse de Riemann. On y étudie la continuité de la projection de la fonction indicatrice de l’intervalle sur un sous-espace vectoriel variable de l’ensemble des fonctions dont le carré est intégrable sur la demi-droite réelle, engendré par des fonctions dilatées de la fonction partie fractionnaire. Plus généralement, étant un élément fixé d’un espace de Hilbert , on étudie l’application qui à un convexe...
Exponential sums and additive problems involving square-free numbers
Exponentialsummen und Nullstellen von L-Reihen.
Extrait d'un travail intitulé «Sur le mémoire de Riemann relatif au nombre des nombres premiers inférieurs à une grandeur donnée»
Farey series and the Riemann hypothesis
Flows of Mellin transforms with periodic integrator
We study Mellin transforms for which is periodic with period in order to investigate ‘flows’ of such functions to Riemann’s and the possibility of proving the Riemann Hypothesis with such an approach. We show that, excepting the trivial case where , the supremum of the real parts of the zeros of any such function is at least .We investigate a particular flow of such functions which converges locally uniformly to as , and show that they exhibit features similar to . For example, ...
Fonctions arithmétiques sur l'anneau des polynômes à coefficients dans un corps fini
From a polynomial Riemann hypothesis to alternating sign matrices.
Gaps between zeros of the derivative of the Riemann -function
Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of . We prove that a positive proportion of gaps are less than times the average spacing and, in the other direction, a positive proportion of gaps are greater than times the average spacing. We also exhibit the existence of infinitely many normalized gaps smaller (larger) than (, respectively).