Uniform Bounds on S-Integral Torsion Points for \mathbbG_m and Elliptic Curves

2023/02/03 by Yap, Jit Wu
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.01562

Abstract

Let K be a number field, S a finite set of places. For \mathbbG_m or an elliptic curve E defined over K, we establish uniformity results on the number of S-integral torsion points relative to a non-torsion point β, as β varies over number fields of bounded degree. In particular for \mathbbG_m, if D is a positive integer, we prove a uniform bound on the degree of a torsion point ζ that is S-integral relative to a non-torsion point β with degree ≤ D.

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