DNA-seminarium: Voronin universality in several complex variables
- Plats: Ångströmlaboratoriet 11167
- Föreläsare: Johan Andersson
- Kontaktperson: Michael Benedicks
Abstract: I discuss my recent proof (work in progress) that the multiple Hurwitz zeta-function with transcendental or rational parameters is universal in several complex variables, giving the first example of a Dirichlet series that is universal in more than one complex variable. I first sketched the proof of the case of transcendental parameters at the Palanga conference on Analytic and Probabalistic methods in Number Theory seven years ago. While I have talked about the case of rational parameters before, during the process of writing up my manuscript I have discovered additional problems, and it is only recently that I have managed to finalize the details of the proof. In particular it turns out that assuming the Generalized Riemann hypothesis greatly simplifes the proof of the rational parameter case; and a substantial amount of extra work is needed in order to obtain the unconditional result.