A Chebyshev criterion for Abelian integrals

El pdf de l'article és la versió preprint: arXiv:0805.1140We present a criterion that provides an easy sufficient condition in order that a collection of Abelian integrals has 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.The first author is partially supported by the MEC/FEDER grant MTM2005-06098-C02-02. The second author by the MEC/FEDER grants MTM2005-02139 and MTM2005-06098 and the C IRIT grant 2005SGR-00550. The third author by the MEC/FEDER grant MTM2005-06098-C02-01 and the CIRIT grant 2 005SGR-0055https://arxiv.org/abs/0805.114