Student Number Theory seminar

Yen-Liang Kuan, National Central University, Taiwan

“On the distribution of torsion points modulo primes.”

Abstract:

Let A be a commutative algebraic group defined over a number field K. For a prime ℘ in K where A has good reduction, let N℘,n be the number of n-torsion F℘-rational points of the reduction of A modulo ℘ where F℘ is the residue field of ℘ and n is a positive integer. When A is of dimension one and n is relative prime to a fixed finite set of primes depending on A/K, we determine the average values of N℘,n as the prime ℘ varies. This average value as function of n always agrees with a divisor function.