Generalized Theta Functions. I. arXiv:1707.03582
Preprint, arXiv:1707.03582 [math-ph] (2017).
Summary: Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential equations for generalized theta functions and finite non-unitary representations of extended Heisenberg group are presented so as other properties and possible applications are pointed out such as a projective embedding of tori by means of generalized theta functions.
MSC:
| 14K25 | Theta functions and abelian varieties |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
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