Torsion points and effective Bogomolov's conjecture

Abstract: 

We give an effective bound to the number of torsion points of  these families of certain groups. Key ingredient in our construction is 

a suitable  Eisenstein series (analytic object). The constant terms of these Eisenstein series encode information about the special values of LL-functions.  The torsion points of these groups are studied by using an explicit description of the special fibers of the the certain curves  due to Edixhoven and Manin-Drinfeld theorem.

The above mentioned  bound is an  effective version of Bogomolov's conjecture. This is a joint work with Chitrabhanu Chowdhuri and Diganta Borah.