Theta functions on tube domains
arXiv:1511.07019 · doi:10.1007/s12188-017-0184-3
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.
Some references added to previous version