Number Theory seminar

Yen-Liang Kuan, Department of Mathematics, University of Waterloo

"On the distribution of torsion points modulo primes"

Let A be a commutative algebraic group dened 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 agrees with a divisor function for almost all n.