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Abstract
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We compute the average size of 2-Selmer groups of the family of hyperelliptic curves
with a marked Weierstrass point over function fields. The result is obtained by a
geometric method which could be considered as a generalization of the one that was
used previously by Q. P. Ho, V. B. Le Hung, and B. C. Ngo (Math. Res. Lett. 21:6
(2014), 1305–1339) to obtain the average size of 2-Selmer groups of elliptic
curves.
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Keywords
2-Selmer group, hyperelliptic curve, function field
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Mathematical Subject Classification
Primary: 11G30, 14H40
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Milestones
Received: 19 January 2019
Revised: 16 March 2021
Accepted: 9 February 2022
Published: 11 September 2022
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