Friday morning talk

[William Stein]

Hi,

Gonzalo's talk is canceled because Gonzalo won't be here. However,
R. Shulze-Pillot will instead speak at the same time (10:30am) on
"Siegel Theta Series and Modular Forms".

William

--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org

[Rainer Schulze-Pillot]

Abstract:

Ordinary theta series count (in their Fourier coefficients) the number
of ways in which the integral positive definite
quadratic form Q(x)=x^t A x in m variables represents an integer n.

Siegel theta series count instead the number of ways in which a given
positive semidefinite g x g - matrix T can be represented as X^t A X
with an integral m x g-Matrix X.

In the same way in which ordinary theta series give modular forms on the
upper half plane for congruence subgroups of SL_2(Z) the Siegel theta
series give modular forms on a g(g+1)/2-dimensional space H_g for the
symplectic group Sp_g(Z) and its congruence subgroups.

Some computations for these have been done by Scharlau, Schiemann, and
myself about 10 years ago; since then nothing much has happened apart
from isolated computations of examples - maybe it's time to start
another systematic attack on the subject.

Greetings
Rainer Schulze-Pillot

William Stein wrote:
> Hi,
>
> Gonzalo's talk is canceled because Gonzalo won't be here. However,

> R. Schulze-Pillot will instead speak at the same time (10:30am) on

> "Siegel Theta Series and Modular Forms".
>
> William
>

--
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Rainer Schulze-Pillot Email: schu...@math.uni-sb.de
FR 6.1 Mathematik
Universitaet des Saarlandes Phone: (+)49 681 302 4835
Postfach 151150 FAX: (+)49 681 302 2789
D-66041 Saarbruecken FAX: (+)49 681 302 4443
WWW: www.math.uni-sb.de/ag/schulze

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