The Square-Free Sieve over Number Fields
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F.Q. Gouvea
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Article
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1993
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Elsevier Science
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English
β 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