The infinitesimal 16th Hilbert problem in dimension zero

被引：9
作者：
Gavrilov, Lubomir
Movasati, Hossein
机构：
[1] Univ Toulouse 3, CNRS, Lab Emile Picard, MIG,UMR 5580, F-31062 Toulouse 9, France
[2] Ochanomizu Univ, Dept Math, Bunkyo Ku, Tokyo 1128610, Japan
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2007年 / 131卷 / 03期
关键词：
Abelian integral; infinitesimal 16th Hilbert problem;
D O I：
10.1016/j.bulsci.2006.04.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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 I(t) defined over Q and its arithmetic properties. Finally, we give necessary and sufficient conditions for an Abelian integral to be identically zero. (c) 2006 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：242 / 257
页数：16
相关论文
共 27 条
[1]  
[Anonymous], 1988, MONOGRAPHS MATH
[2]   The equation f(X) = f(Y) in rational functions X = X(t), Y = Y(t) [J].
Avanzi, RM ;
Zannier, UM .
COMPOSITIO MATHEMATICA, 2003, 139 (03) :263-295
[3]   Relative differential forms and complex polynomials [J].
Bonnet, P ;
Dimca, A .
BULLETIN DES SCIENCES MATHEMATIQUES, 2000, 124 (07) :557-571
[4]  
Bost JB, 1996, ASTERISQUE, P115
[5]   MONODROMY OF ISOLATED HYPERSURFACE SINGULARITIES [J].
BRIESKOR.E .
MANUSCRIPTA MATHEMATICA, 1970, 2 (02) :103-&
[6]   Algebraic Gauss-Manin systems and Brieskorn modules [J].
Dimca, A ;
Saito, M .
AMERICAN JOURNAL OF MATHEMATICS, 2001, 123 (01) :163-184
[7]   Petrov modules and zeros of Abelian integrals [J].
Gavrilov, L .
BULLETIN DES SCIENCES MATHEMATIQUES, 1998, 122 (08) :571-584
[8]   The displacement map associated to polynomial unfoldings of planar Hamiltonian vector fields [J].
Gavrilov, L ;
Iliev, ID .
AMERICAN JOURNAL OF MATHEMATICS, 2005, 127 (06) :1153-1190
[9]   The infinitesimal 16th Hilbert problem in the quadratic case [J].
Gavrilov, L .
INVENTIONES MATHEMATICAE, 2001, 143 (03) :449-497
[10]  
GAVRILOV L, 2005, ANN FAC SCI TOULOUSE, V14, P677
123