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Difference between revisions of "Quasi-Abelian function"

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A generalization of an [[Abelian function|Abelian function]]. A [[Meromorphic function|meromorphic function]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076350/q0763501.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076350/q0763502.png" />, in the complex space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076350/q0763503.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076350/q0763504.png" />, is called a quasi-Abelian function if it has <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076350/q0763505.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076350/q0763506.png" />, linearly independent periods; in the case of Abelian functions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/q/q076/q076350/q0763507.png" />. Quasi-Abelian functions can be regarded as a limiting case of Abelian functions when certain periods increase unboundedly.
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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>

Latest 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
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article