数学科学系

Department of Mathematical Sciences

Effective bounds for integral points on modular curves

 

报告题目: Effective bounds for integral points on modular curves

 

报告人: 沙敏(Ph.D of Université Bordeaux 1)

 

时间:20131010(星期四)16:00-17:00   

 

地点:理科楼数学系A304

 

摘要:  Let C be a modular curve corresponding to a congruence subgroup and defined over a number field K, and j its j-invariant. For a K-rational point P on C, we call it integral if j(P) is an algebraic integer. By Siegel's Theorem, the curve C has finitely many integral points if its genus is nonzero or j has at least three cusps. But currently there is no effective form of Siegel's Theorem in the sense that it implies no effective or explicit bounds for the size of integral points. In this talk, we will present several such effective or explicit bounds in the case of modular curves and illustrate some applications.

 

联系人:印林生