## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, May 22, 2012 — 10:00 AM to 12:00 PM EDT

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.

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.