Deux extensions de Théorèmes de Hamburger

Details Deux extensions de Théorèmes de Hamburger Deux extensions de Théorèmes de Hamburger

2011-06-23

arxiv.org/abs/1106.4749v2

Mathematics

Number Theory

14 pages, in French. CRM preprint 1027. Introduction slightly improved

Scientific paper

10.1016/j.exmath.2012.03.003

We propose two types of extensions to Hamburger's theorems on the Dirichlet series with functional equation like the one of the Riemann zeta function, under weaker hypotheses. This builds upon the dictionary betweeen the moderate meromorphic functions with functional equation and the tempered distributions with extended S-support condition. ----- Nous proposons deux types d'extensions aux th\'eor\`emes de Hamburger sur les s\'eries de Dirichlet avec \'equation fonctionnelle comme celle de la fonction z\^eta de Riemann, sous des hypoth\`eses plus faibles. Ceci repose sur le dictionnaire entre les fonctions m\'eromorphes mod\'er\'ees avec cette \'equation fonctionnelle et les distributions temp\'er\'ees avec la condition de support S-\'etendue.

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