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SUMMARY:Christina Roehrig (Universität zu Köln)
DTSTART:20210204T140000Z
DTEND:20210204T150000Z
DTSTAMP:20260423T024721Z
UID:UCDANT/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCDANT/10/">
 Siegel theta series for indefinite quadratic forms</a>\nby Christina Roehr
 ig (Universität zu Köln) as part of Dublin Algebra and Number Theory Sem
 inar\n\n\nAbstract\nIn this talk\, we will give an insight into the field 
 of Siegel modular forms. As they occur as a generalization of elliptic mod
 ular forms\, some results can be transferred from the well-known theory de
 veloped for these functions. We examine a  result by Vignéras\, who showe
 d that there is a quite simple way to determine whether a certain theta-se
 ries admits modular transformation properties. To be more specific\, she s
 howed that solving a differential equation of second order serves as a cri
 terion for modularity. We generalize this result for Siegel theta-series.\
 n\nIn order to do so\, we construct Siegel theta-series for indefinite qua
 dratic forms by considering functions that solve an $n\\times n$-system of
  partial differential equations. These functions do not only give examples
  of Siegel theta-series\, but we can even determine a basis of  Schwartz f
 unctions that generate series which transform like modular forms.\n
LOCATION:https://researchseminars.org/talk/UCDANT/10/
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