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SUMMARY:Athanasios Sourmelidis (Graz University of Technology)
DTSTART:20240520T110000Z
DTEND:20240520T120000Z
DTSTAMP:20260423T021333Z
UID:GANT/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GANT/63/">On
  the interface of universal zeta-functions and frequently hypercyclic vect
 ors of translation operators</a>\nby Athanasios Sourmelidis (Graz Universi
 ty of Technology) as part of Greek Algebra & Number Theory Seminar\n\n\nAb
 stract\nIf $\\Omega \\subseteq \\mathbb{C}$ is a simply connected domain a
 nd $H(\\Omega)$ is the Fréchet space of holomorphic functions on $\\Omega
 $\, then it is well-known from linear dynamics that there is a dense $G_{\
 \delta}$ set of $H(\\Omega)$ such that for any element $f$ from this set\,
  the set $\\{f( \\cdot + i\\tau ) : \\tau \\in \\mathbb{R} \\}$ is dense i
 n $H(\\Omega)$. However\, no information is provided on how these elements
  $f$ look like. Despite that\, in the special case when $\\Omega$ is\nthe 
 vertical strip of complex numbers with real part between $1/2$ and $1$\, S
 ergei Voronin proved using analytic number theoretical methods that the Ri
 emann zeta-function $\\zeta$ is universal in the sense that the set $\\{\\
 log \\zeta( \\cdot + i\\tau ) : \\tau \\in \\mathbb{R} \\}$ is dense in $H
 (\\Omega)$. This phenomenon has now been observed for a large class of “
 zeta-functions”. In these talks I will discuss about the aforementioned 
 results and draw connections between the theory of translation operators a
 nd the theory of universal zeta-functions in the form of applications and 
 research questions.\n
LOCATION:https://researchseminars.org/talk/GANT/63/
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