Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Christina Röhrig
Affiliation:

Universität zu Köln
Date:

Wed, 02/06/2021 - 14:30 - 15:30 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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/246