Abstract
AbstractLet E be an elliptic curve, and let Ln be the Kummer extension generated by a primitive pnth root of unity and a pn-th root of a for a fixed a ∈ ℚ× − ﹛±﹜1﹜. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of E over Ln in certain cases. The aim of this note is to explain how some of these predictions might be accounted for by Heegner points arising from a varying collection of Shimura curve parametrisations.
Publisher
Canadian Mathematical Society
Cited by
6 articles.
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1
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