Difference between revisions of "Quasi-Abelian function"
From Encyclopedia of Mathematics
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| − | A generalization of an [[Abelian function|Abelian function]]. A [[Meromorphic function|meromorphic function]] | + | {{TEX|done}} |
| + | A generalization of an [[Abelian function|Abelian function]]. A [[Meromorphic function|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. | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> F. Severi, "Funzioni quasi abeliane" , Città del Vaticano (1947)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> F. Severi, "Funzioni quasi abeliane" , Città del Vaticano (1947)</TD></TR></table> | ||
Revision as of 11:42, 5 July 2014
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.
References
| [1] | F. Severi, "Funzioni quasi abeliane" , Città del Vaticano (1947) |
How to Cite This Entry:
Quasi-Abelian function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-Abelian_function&oldid=17494
Quasi-Abelian function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-Abelian_function&oldid=17494
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article