Di, 20.11.2012, 16:15
Linear characters of Hilbert Modular Groups and associated automorphic forms
AG-Seminar Algebra

Referent: Hatice Boylan (Siegen/Aachen)
Raum: S215 - 401

 According to a general philosophy to a linear character of
an arithmetic group there should be associated an interesting
automorphic form transforming under the given group with this
character. The most prominent example for this is the group SL(2,Z)
(or rather its double cover Mp(2,Z)) and the Dedekind eta function. A
natural question is for the situation for the Hilbert modular groups.
Surprisingly, the linear characters of the Hilbert modular groups were
not known until recently. In this talk, we shall report about recent
joint work with Nils Skoruppa, where we determined all linear
characters of the Hilbert modular groups. Furthermore, I shall explain
that to these characters correspond indeed automorphic forms (which I
found in my thesis). These automorphic forms can be regarded as analogues of the famous Jacobi theta function which occurs in the
Jacobi triple product identity. The first Taylor coefficients of these new functions are candidates for generalizing the Dedekind eta
function to number fields.



Fachbereich Mathematik
Technische Universität Darmstadt

Schlossgartenstraße 7
64289 Darmstadt

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