Remarks on the LindelÖf Hypothesis
Répartition des zéros des fonctions et matrices aléatoires
Second moments of Dirichlet -functions weighted by Kloosterman sums
For the general modulo and a general multiplicative character modulo , the upper bound estimate of is a very complex and difficult problem. In most cases, the Weil type bound for is valid, but there are some counterexamples. Although the value distribution of is very complicated, it also exhibits many good distribution properties in some number theory problems. The main purpose of this paper is using the estimate for -th Kloosterman sums and analytic method to study the asymptotic properties...
Séries de Dirichlet associées à des fractions rationnelles de plusieurs variables
Séries hypergéométriques et irrationalité des valeurs de la fonction zêta de Riemann
Nous effectuons un survol des résultats connus sur la nature diophantienne des valeurs de la fonction zêta de Riemann aux entiers. Nous mettons en particulier l’accent sur le rôle important des séries hypergéométriques dans les démonstrations de l’irrationalité de et d’une infinité des nombres .
Séries hypergéométriques multiples et polyzêtas
Nous décrivons un algorithme théorique et effectif permettant de démontrer que des séries et intégrales hypergéométriques multiples relativement générales se décomposent en combinaisons linéaires à coefficients rationnels de polyzêtas.
Sieve methods and class-number probelms. II.
Sieve methods and class-number problems III.
Sign-changes of the Thue-Morse Fractal Function and Dirichlet L-Series.
Simple zeros of the zeta function of a quadratic number field. I.
Simultaneous generation of Koecher and Almkvist-Granville's Apéry-like formulae.
Small gaps between zeros of twisted L-functions
Small values of the Riemann zeta function on the critical line
We investigate real values of the Riemann zeta function on the critical line. We show that if Gram's points do not intersect with the ordinates of the nontrivial zeros of the Riemann zeta function then the Riemann zeta function takes arbitrarily small real values on the critical line.
Some definite integrals associated with the Riemann zeta function.
Some formulas for the Riemann zeta function at odd integer argument resulting from Fourier expansions of the Epstein zeta function
Some identities involving the Dirichlet L-function
Some new estimates in the Dirichlet divisor problem
Some problems concerning roots of polynomials with Dirichlet characters as coefficients
Some problems on mean values of the Riemann zeta-function
Several problems and results on mean values of are discussed. These include mean values of and the fourth moment of for .
Some remarks on the distribution of a sequence connected with .