Bounding the number of zeros of certain Abelian integrals |
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Authors: | F. Mañ osas |
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Affiliation: | a Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain b Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Barcelona, Spain |
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Abstract: | In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n+k−1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way. |
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Keywords: | primary, 34C07, 34C08 secondary, 41A50 |
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