Quasi-Abelian function

From Encyclopedia of Mathematics
Jump to: navigation, search

A generalization of an Abelian function. A meromorphic function $f(z)$, $z=(z_1,\ldots,z_n)$, in the complex space $\mathbf C^n$, $n>1$, is called a quasi-Abelian function if it has $m$, $0<m\leq2n$, linearly independent periods; in the case of Abelian functions $m=2n$. Quasi-Abelian functions can be regarded as a limiting case of Abelian functions when certain periods increase unboundedly.


[1] F. Severi, "Funzioni quasi abeliane" , Città del Vaticano (1947)
How to Cite This Entry:
Quasi-Abelian function. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article