The Chebyshev Property of Some Complete Hyper-elliptic Integrals of the First Kind

讲座时间 Datetime: 2022年6月18日，星期六， 15:00-16:00

地点 Venue: 腾讯线上会议：491-363-147

 主持人 Host：王少卿

报告人 Speaker:孙杨剑 

单位 Affiliation:上饶师范学院

报告摘要 Abstract:

In this talk, we provide a criterion to determine the Chebyshev property for some complete Abelian integrals of the first kind. As an application, we study some classes of complete hyper-elliptic integrals of the first kind, which are some degenerate subfamilies of a family considered in the work of Gavrilov and Iliev(2003, Trans.。Amer. Math. Soc. 356, 1185-1207). It is shown that exist for the degenerate subfamilies of ovals around the center (1,0) of the hyper-elliptic Hamiltonian which are not exceptional families proposed by Gavrilov and Iliev, the corresponding complete hyper-elliptic integrals of the first kind still satisfy the Chebyshev property.