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Siegel modular forms of small weight and the Witt operator. (English) Zbl 1244.11049

Baeza, Ricardo (ed.) et al., Quadratic forms – algebra, arithmetic, and geometry. Based on the international conference on the algebraic and arithmetic theory of quadratic forms, Frutillar, Chile, December 13–19, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4648-3/pbk). Contemporary Mathematics 493, 189-209 (2009).
Summary: To calculate dimensions of Siegel modular forms including non-cusp forms, we determine the image of Siegel Phi-operator for small weight which were unknown in general theory. We treat the case of the Hecke type group of prime level and also vector valued Siegel modular forms of level one of degree two. For this purpose we propose a new basis problem on theta functions related with the Witt operator. We also show the surjectivity of the Witt operator in case of vector valued Siegel modular forms of level one for big weight by giving certain new dimension formulas of Siegel modular forms. We also give new upper and lower bounds of unknown dimensions of vector valued Siegel modular forms of small weight.
For the entire collection see [Zbl 1170.11001].

MSC:

11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F27 Theta series; Weil representation; theta correspondences
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