a1 Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan (email: email@example.com)
a2 Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan (email: firstname.lastname@example.org)
Let be a commutative algebraic group defined over a number field K. For a prime ℘ in K where has good reduction, let N ℘,n be the number of n-torsion points of the reduction of modulo ℘ where n is a positive integer. When is of dimension one and n is relatively prime to a fixed finite set of primes depending on , we determine the average values of N ℘,n as the prime ℘ varies. This average value as a function of n always agrees with a divisor function.
(Received October 31 2011)
2010 Mathematics subject classification
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Research partially supported by National Science Council, Republic of China.