On meromorphic mappings admitting an Algebraic Addition Theorem
نویسنده
چکیده
A proper or singular abelian mapping from C to C n is parametrized by n meromorphic functions with at most 2n periods. We develop the existence and structure theorems of the classical theory of an abelian mapping purely on the basis of its defining functional equation, the so-called algebraic addition theorem (AAT), with no appeal to any representation as quotients of theta functions. We offer two new proofs of the periodicity of a nonrational mapping admitting an AAT. We also prove by new arguments the existence of a rational group law on an associated algebraic variety, and that all proper and singular abelian mappings do admit an AAT.
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