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Computing a square root for the number field sieve

✍ Scribed by Couveignes.


Book ID
127401597
Tongue
English
Weight
37 KB
Category
Library

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πŸ“œ SIMILAR VOLUMES


The Square-Free Sieve over Number Fields
✍ F.Q. Gouvea πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 442 KB

For \(E\) an elliptic curve over a number field \(K\), we give a lower bound, conditional on the "parity conjecture." for the number of quadratic twists of \(E\) whose Mordell-Weil rank is at least two. The main tool is a sieve-theoretic estimate of the number of square-free values of a homogeneous