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The Square-Free Sieve over Number Fields

✍ Scribed by F.Q. Gouvea

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
442 KB
Volume
43
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 binary form. The results are a direct extension of those found by the author and B. Mazur (J. Amer. Muth. Soc. 4, 1991, 1-23). (: 1993 Academic Press, Inc.

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