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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: The linear characters of the Hilbert modular groups and associated automorphic forms

Presented by Nils Skoruppa, University of Siegen

29 October 2012 16:00 in CM221

The linear characters of the elliptic modular group SL(2,Z)
are since long well-known and occur in many contexts. The group of
these characters is generated by the character which shows up in the
transformation law of the famous Dedekind eta function, which plays a
fundamental role in theories ranging from complex multiplication over
elliptic curves to infinite dimensional Lie algebras. In contrast to
this, the linear characters of the general Hilbert modular groups
SL(2,O), where O is the ring of integers of a number field, seemed
never to have gained sufficient interest. In fact, they have never
been explicitly determined. In recent work we obtained an explicit
description of the groups of linear characters of the Hilbert modular
groups, and we found also interesting automorphic functions associated
to these characters, which are in several aspects analogous to the
Dedekind eta function.

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