# 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> |

## 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