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Siegel theta series for indefinite quadratic forms

Posted in
Speaker: 
Christina Röhrig
Affiliation: 
Universität zu Köln
Date: 
Wed, 2021-06-02 14:30 - 15:30
Parent event: 
Number theory lunch seminar

Due to a result by Vignéras from 1977, there is a quite simple way to determine
whether a certain theta series admits modular transformation properties: she
showed that solving a differential equation of second order serves as a criterion
for modularity. We generalize this result to Siegel theta series of arbitrary genus
n. In order to do so, we construct Siegel theta series for indefinite quadratic
forms of signature (r, s) by considering polynomials with a certain homogeneity
property. In general, we obtain non-holomorphic functions, so we will also
investigate the special case s = 1 and give a description of the holomorphic part
of the series.

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