Title: Generalized Theta Functions. I,
Abstract: 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.