### Abstract

Let H be a polynomial of degree m+. 1 on C2 such that its generic fiber is biholomorphic to C*, and let ω be an arbitrary polynomial 1-form of degree n on C2. We give an upper bound depending only on m and n for the number of isolated zeros of the complete Abelian integral defined by H and ω. © 2012 Elsevier Ltd.

Original language | English |
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Pages (from-to) | 562-570 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 394 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Oct 2012 |

### Keywords

- Abelian integrals
- Weak Hilbert's 16th problem

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## Cite this

Rebollo-Perdomo, S. (2012). Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to C*.

*Journal of Mathematical Analysis and Applications*,*394*(2), 562-570. https://doi.org/10.1016/j.jmaa.2012.05.014