The exact bounds on the number of zeros of complete hyperelliptic integrals of the first kind

被引：11
|
作者：
Wang, Na [1 ]
Wang, Jihua [1 ]
Xiao, Dongmei [1 ]
机构：
[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 254卷 / 02期
关键词：
The exact bounds; The number of zeros; Hyperelliptic integrals; The first kind; Chebyshev; ELLIPTIC INTEGRALS; ABELIAN-INTEGRALS; NON-OSCILLATION; DEGREE-4; PERTURBATIONS; PROPERTY; LOOP;
D O I：
10.1016/j.jde.2012.07.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study three classes of complete hyperelliptic integrals of the first kind, which are some degenerate subfamilies of a family considered in the work of Gavrilov and Him It is shown that the three classes of complete hyperelliptic integrals are Chebyshev, and the exact bounds on the number of zeros of these Abelian integrals are one. This result reveals that there exist degenerate subfamilies of ovals of the hyperelliptic Hamiltonian which are not exceptional families proposed by Gavrilov and Iliev, but the corresponding complete hyperelliptic integrals of the first kind still satisfy the Chebyshev property. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：323 / 341
页数：19
相关论文
共 50 条
12345