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...
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| Format: | Article |
| Language: | English |
| Published: |
Princeton University Press,
2015-01-22T19:12:32Z.
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| Subjects: | |
| Online Access: | Get fulltext |