The infinitesimal 16th Hilbert problem in dimension zero
经典分析与常微分方程
2010-07-27 v1 数论
摘要
We study the analogue of the infinitesimal 16th Hilbert problem in dimension zero. Lower and upper bounds for the number of the zeros of the corresponding Abelian integrals (which are algebraic functions) are found. We study the relation between the vanishing of an Abelian integral defined over and its arithmetic properties. Finally, we give necessary and sufficient conditions for an Abelian integral to be identically zero.
引用
@article{arxiv.math/0507061,
title = {The infinitesimal 16th Hilbert problem in dimension zero},
author = {Lubomir Gavrilov and Hossein Movasati},
journal= {arXiv preprint arXiv:math/0507061},
year = {2010}
}
备注
21 pages