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arXiv · 1511.07019

Theta functions on tube domains

Josef F. Dorfmeister·Sebastian Walcher
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Abstract

We discuss generalizations of classical theta series, requiring only some basic properties of the classical setting. As it turns out, the existence of a generalized theta transformation formula implies that the series is defined over a quasi-symmetric Siegel domain. In particular the exceptional symmetric tube domain does not admit a theta function.

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Josef F. Dorfmeister, Sebastian Walcher. 2015-11-22. Theta functions on tube domains. https://doi.org/10.1007/s12188-017-0184-3

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