Most odd degree hyperelliptic curves have only one rational point
Consider the smooth projective models C of curves y [superscript 2] = f(x) with f(x) ∈Z[x] monic and separable of degree 2g+1. We prove that for g ≥ 3, a positive fraction of these have only one rational point, the point at infinity. We prove a lower bound on this fraction that tends to 1 as g→∞. Fi...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
| Published: |
Princeton University Press
2015
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| Online Access: | http://hdl.handle.net/1721.1/93149 https://orcid.org/0000-0002-8593-2792 |