The exact bounds on the number of zeros of complete hyperelliptic integrals of the first kind
The exact bounds on the number of zeros of complete hyperelliptic integrals of the first kind
复制标题
DOI：
10.1016/j.jde.2012.07.011
复制
发表时间：
2013-01
影响因子：
2.4
通讯作者：
Na Wang;Jihua Wang;Dongmei Xiao
中科院分区：
文献类型：
--
作者：
Na Wang;Jihua Wang;Dongmei Xiao
本文研究了三类第一类完全超椭圆积分，它们是Gavrilov和Iliev工作中考虑的一族的一些退化子族。证明了这三类完全超椭圆积分都是切比雪夫的，并且这些阿贝尔积分的零点个数的精确界是1。这一结果揭示了超椭圆哈密顿量存在退化的椭圆子族，它们不是Gavrilov和Iliev提出的例外族，但相应的第一类完全超椭圆积分仍然满足Chebyshev性质。
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 Iliev. 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.