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Preprint (Vorabdruck) zugänglich unter
Global distributions and special zeta values
URN: urn:nbn:de:bsz:291-scidok-42977
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4297/
pdf-Format:
Dokument 1.pdf (313 KB)
Institut:
Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe:
Mathematik
Dokumentart:
Preprint (Vorabdruck)
Schriftenreihe:
Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer:
16
Sprache:
Englisch
Erstellungsjahr:
2000
Publikationsdatum:
18.11.2011
Kurzfassung auf Englisch:
In this paper, we develop the theory of global distributions (i.e. distributions of global fields) and apply it to the study of special values of abelian L-functions of a number field and division points of rank one Drinfeld modules. We introduce the concept of \epsilon-distributions and give examples by \epsilon-partial zeta functions. We determine the ranks of level groups of various kinds of universal distributions of a global field k, such as universal \epsilon-, punctured, punctured even and odd distributions of k. We show the universality of several distributions derived from special values of the \epsilon-partial zeta functions by studying \mathbb{Q}-linear independence of some special values. We also propose a conjecture and a question about the universality of \epsilon-distributions of special values of \epsilon-partial zeta functions.
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