On the size of the Jacobians of curves over finite fields

Igor Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Given a smooth curve of genus g ≥ 1 which admits a smooth projective embedding of dimension m over the ground field Fq of q elements, we obtain the asymptotic formula q g+o(g) for the size of set of the Fq -rational points on its Jacobian in the case when m and q are bounded and g → ∞. We also obtain a similar result for curves of bounded gonality. For example, this applies to the Jacobian of a hyperelliptic curve of genus g → ∞.

Original languageEnglish
Pages (from-to)587-595
Number of pages9
JournalBulletin of the Brazilian Mathematical Society
Issue number4
Publication statusPublished - Dec 2008


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