IMPRESSUM   DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
p-adic Numbers, p-adic Analysis, and Zeta-Functions Semester WiSe 2017 / 18 Dozent Klaus Kuennemann Veranstaltungsart Seminar Inhalt Let p be a prime number. We start with the introduction of the field Q_p of p-adic numbers. Afterwards we discuss p-adic interpolation of the Riemann zeta-function and construct a non-archimedean analog of the field of complex numbers. Using p-adic power series we introduce logarithm, gamma, and exponential functions. As a highlight we show the rationality of the zeta-function of a set of equations over finite field. This rationality is part of the famous Weil conjectures and was first shown by Dwork in 1960. Literaturangaben Neal Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions, Springer 1984 Empfohlene Vorkenntnisse Algebra and some complex analysis, talks in the second half might also require more commutative algebra and some algebraic number theory Termin Tue 16h00 -17h30 Anmeldung Vorbesprechung/Themenvergabe: Organisational meeting/distribution of topics: Thursday July 27th 2017 at 12h00h in room M201 or contact my assistant Martino Stoffel or me by email Anmeldung zu Studienleistungen/Prüfungsleistungen: FlexNow Studienleistungen Presentation: Giving a seminar talk of roughly 90 minutes Prüfungsleistungen Detailed written report of the seminar talk Regelungen bei Studienbeginn vor WS 2015 / 16 Benotet: O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung Unbenotet: O. g. Studienleistung Module BSem, MV, MSem, LA-GySem ECTS Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16