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Experimental Mathematics Volume 9, 2000 - Issue 4
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Original Articles

Ranks of Elliptic Curves in Families of Quadratic Twists

Karl Rubin Department of Mathematics, Stanford University, Stanford, CA, 94305, United States E-mail: [email protected]
&
Alice Silverberg Department of Mathematics, Ohio State University, Columbus, OH, 43210, United States E-mail: [email protected]
Pages 583-590 | Published online: 04 Apr 2012
 
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Abstract

We show that the unboundedness of the ranks of the quadratic twists of an elliptic curve is equivalent to the divergence of certain infinite series.

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