Title: The probability that the number of points on the Jacobian of a genus 2 curve is prime
Authors: Castryck, Wouter * ×
Folsom, Amanda *
Hubrechts, Hendrik *
Sutherland, Andrew V. * #
Issue Date: 2012
Publisher: Oxford University Press
Series Title: Proceedings of the London Mathematical Society vol:104 issue:6 pages:1235-1270
Abstract: In 2000, Galbraith and McKee heuristically derived a formula that estimates the probability that a randomly chosen elliptic curve over a xed nite prime eld has a prime number of rational points. We show how their heuristics can be generalized to Jacobians of curves of higher genus. We then elaborate this in genus g = 2 and study various related issues, such as the probability of cyclicity and the probability of primality of the number of points on the
curve itself. Finally, we discuss the asymptotic behavior for g --> 1.
ISSN: 0024-6115
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
* (joint) first author
× corresponding author
# (joint) last author

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