A Chebyshev criterion for Abelian integrals

Grau, M.; Mañosas, F.; Villadelprat, J.

doi:10.1090/S0002-9947-2010-05007-X

A Chebyshev criterion for Abelian integrals
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by M. Grau, F. Mañosas and J. Villadelprat

Trans. Amer. Math. Soc. 363 (2011), 109-129

DOI: https://doi.org/10.1090/S0002-9947-2010-05007-X

Published electronically: August 27, 2010

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Abstract:

We present a criterion that provides an easy sufficient condition in order for a collection of Abelian integrals to have the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be checked, in many cases, in a purely algebraic way. By using this criterion, several known results are obtained in a shorter way and some new results, which could not be tackled by the known standard methods, can also be deduced.

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