Dokument: Uniform Rationality for Compact p-adic Analytic Groups
| Titel: | Uniform Rationality for Compact p-adic Analytic Groups | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=60187 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20220719-110447-6 | |||||||
| Kollektion: | Dissertationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Abschlussarbeiten » Dissertation | |||||||
| Medientyp: | Text | |||||||
| Autor: | M.Sc. Kısakürek, Zeynep [Autor] | |||||||
| Dateien: |
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| Beitragende: | Prof. Dr. Halupczok, Immanuel [Gutachter] Prof. Dr. Reineke, Markus [Gutachter] | |||||||
| Dewey Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik » 510 Mathematik | |||||||
| Beschreibung: | For a given group G, one can encode the asymptotic behavior of r_n(G) denoting the number of isomorphism classes of complex irreducible n-dimensional representations of G in a Dirichlet series. This generating series is called the representation zeta function of G, and it is used to investigate the distribution of character degrees. Stasinski and Zordan proved that this series is a virtually rational function in p^{-s} for a FAb compact $p$-adic analytic group.
The (virtual) rationality of such representation zeta functions is obtained by the rationality of a reduced zeta series called partial zeta series. In this work, we consider these partial zeta series for a family of FAb compact p-adic analytic groups. We impose the condition that there exists an analytic formula uniformly defining the family of FAb compact p-adic analytic groups, and first show how to obtain a uniformly powerful pro-p subgroup of a given p-adic analytic group in a uniformly definable way for p > 2. Following this, we prove that the partial zeta series are uniformly rational. | |||||||
| Lizenz: |  Urheberrechtsschutz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Algebra und Zahlentheorie | |||||||
| Dokument erstellt am: | 19.07.2022 | |||||||
| Dateien geändert am: | 19.07.2022 | |||||||
| Promotionsantrag am: | 19.04.2022 | |||||||
| Datum der Promotion: | 30.05.2022 |
