Student Number Theory seminar

Yen-Liang Kuan, National Central University, Taiwan

"On the distribution of torsion points modulo primes - Part II."

Let A be a commutative algebraic group dened over a number eld 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 eld of } and n is a positive integer. When A is of dimension one
and n is relative prime to a xed nite 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.