On the distribution of torsion points modulo primes

Yen Mei J. Chen, Yen Liang Kuan

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Let $\Bbb A$ be a commutative algebraic group defined over a number field K. For a prime ain K where $\Bbb A$ has good reduction, let N a,n be the number of n-torsion points of the reduction of $\Bbb A$ modulo awhere n is a positive integer. When $\Bbb A$ is of dimension one and n is relatively prime to a fixed finite set of primes depending on $\BbbA{/K}$, we determine the average values of N a,n as the prime avaries. This average value as a function of n always agrees with a divisor function.

Original languageEnglish
Pages (from-to)339-347
Number of pages9
JournalBulletin of the Australian Mathematical Society
Issue number2
StatePublished - Oct 2012


  • algebraic groups
  • complex multiplication
  • elliptic curves
  • number fields
  • torsion points


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