Difference between revisions of "Quasi-Abelian function"
From Encyclopedia of Mathematics
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| − | A generalization of an [[ | + | 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. |
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Latest revision as of 19:20, 6 December 2023
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) Zbl 0041.48201 |
How to Cite This Entry:
Quasi-Abelian function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-Abelian_function&oldid=54746
Quasi-Abelian function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-Abelian_function&oldid=54746
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article