Siegel theta series for quadratic forms of signature $(m-1,1)$

Christina Roehrig

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arXiv · 2106.05703

Siegel theta series for quadratic forms of signature $(m-1,1)$

Christina Roehrig

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Abstract

We investigate Siegel theta series for quadratic forms of signature $(m-1,1)$. On the one hand, we construct a holomorphic series that does not transform like a modular form. On the other hand, we construct a non-holomorphic series that transforms like a Siegel modular form of weight $m/2$. Moreover, the holomorphic series describes almost everywhere the holomorphic part of the modular series.

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Christina Roehrig. 2021-06-10. Siegel theta series for quadratic forms of signature $(m-1,1)$. https://arxiv.org/abs/2106.05703

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