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[20/05/2024] GANT Seminar – Athanasios Sourmelidis (TU Graz), On the interface of universal zeta-functions and frequently hypercyclic vectors of translation operators

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Dear all,
The next series of talks in GANT seminar is given by Athanasios Sourmelidis (TU Graz) with first talk on Monday 20 May 2024, 2-3pm (Time in Greece, GMT+2). 
Title: On the interface of universal zeta-functions and frequently hypercyclic vectors of translation operators

Abstract: If \Omega \subseteq \mathbb{C} is a simply connected domain and 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 in H(\Omega). However, no information is provided on how these elements f look like. Despite that, in the special case when \Omega is

the vertical strip of complex numbers with real part between 1/2 and 1, Sergei Voronin proved using analytic number theoretical methods that the Riemann 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 and the theory of universal zeta-functions in the form of applications and research questions.

Zoom link: https://authgr.zoom.us/j/2586769419?pwd=dElhRGxrRlh0V003emc3ejRjSVZrUT09
Meeting ID: 258 676 9419
Passcode: 908335
The organizers,

 
Dimitrios Chatzakos
Maria Chlouveraki
Ioannis Dokas
Angelos Koutsianas
Chrysostomos Psaroudakis