2016/10/26 by Dorin Ghişa, Dorin Ghisa, Ghisa, Dorin
Mathematics · #Holomorphic and Operator Theory #Mathematics and Applications #Meromorphic and Entire Functions #math.CV #msc:11M26 #msc:30C35
paper · pdf · doi:10.48550/arxiv.1611.01082
22 pages, 9 figures
arxiv created 2016/11/15 · arxiv updated 2016/11/17
We dealt in a series of previous publications with some geometric aspects of the mappings by functions obtained as analytic continuations to the whole complex plane of general Dirichlet series. Pictures illustrating those aspects contain a lot of other information which has been waiting for a rigorous proof. Such a task is partially fulfilled in this paper, where we succeeded among other things, to prove a theorem about general Dirichlet series having as corollary the Speiser's theorem. We have also proved that those functions do not possess multiple zeros of order higher than 2 and the double zeros have very particular locations. Moreover, their derivatives have only simple zeros. With these results at hand, we revisited GRH for a simplified proof.