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arXiv · 1207.1673

Rankin-Selberg L-functions in cyclotomic towers, II

Jeanine Van Order
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Abstract

Following the prequel work \cite{VO3}, we prove a generalization of "Mazur's conjecture" for $L$-functions of elliptic curves in abelian extensions of imaginary quadratic fields, including the assertion that the Mordell-Weil rank of an elliptic curve in the ${\bf{Z}}_p^2$-extension is finitely generated modulo Heegner points. The novelty of the approach here is to use the existence of a suitable $p$-adic $L$-function to reduce the problem to a minimal nonvanishing criterion, which should be applicable to a broader class of problems than considered here.

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Jeanine Van Order. 2012-07-06. Rankin-Selberg L-functions in cyclotomic towers, II. https://arxiv.org/abs/1207.1673

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