On curves over finite fields with Jacobians of small exponent

Kevin Ford*, Igor Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We show that finite fields over which there is a curve of a given genus g ≥ 1 with its Jacobian having a small exponent, are very rare. This extends a recent result of Duke in the case of g = 1. We also show that when g = 1 or g = 2, our lower bounds on the exponent, valid for almost all finite fields Fq and all curves over Fq, are best possible.

Original languageEnglish
Pages (from-to)819-826
Number of pages8
JournalInternational Journal of Number Theory
Volume4
Issue number5
DOIs
Publication statusPublished - 2008

Keywords

  • Distribution of divisors
  • Group structure
  • Jacobian

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