Zero sums in finite cyclic groups.
B. Poonen a récemment exhibé des exemples de variétés projectives et lisses de dimension 3 sur un corps de nombres qui n’ont pas de point rationnel et pour lesquelles il n’y a pas d’obstruction de Brauer–Manin après revêtement fini étale. Je montre que les variétés qu’il construit possèdent des zéro-cycles de degré 1.
Under certain mild analytic assumptions one obtains a lower bound, essentially of order , for the number of zeros and poles of a Dirichlet series in a disk of radius . A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.
Introduction. In 1974, N. Levinson showed that at least 1/3 of the zeros of the Riemann ζ-function are on the critical line ([19]). Today it is known (Conrey, [6]) that at least 40.77% of the zeros of ζ(s) are on the critical line and at least 40.1% are on the critical line and are simple. In [16] and [17], Hilano showed that Levinson's original result is also valid for Dirichlet L-series. This paper is a shortened version of parts of the dissertation [3], the full details of...