Elliptic curves and special values of \(L\)-series
type: Item
instance of: scholarly article
title: Elliptic curves and special values of \(L\)-series
zbMATH Open document ID: 0865.11047
author: Massimo Bertolini
published in: Collectanea Mathematica
publication date: 1996-11-21T00:00:00Z
full work available at URL: https://eudml.org/doc/40473
review text: Let \(E/ \mathbb{Q}\) be a modular elliptic curve, and let \(L(E/ \mathbb{Q},s)\) be its Hasse-Weil \(L\)-series. Following the methods of joint work of the author with Henri Darmon, and working under certain simplifying assumptions, it is proved that \(L(E/ \mathbb{Q}, 1)\neq 0\) implies that \(E(\mathbb{Q})\) is finite. The method of proof uses a result of B. Gross on the special value of the \(L\)-series of \(E\) over an imaginary quadratic field, and a result of B. Edixhoven on the image of Heegner points in the groups of connected components of modular Jacobians.
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 14H25
zbMATH DE Number: 937448
zbMATH Keywords: modular elliptic curve
zbMATH Keywords: Hasse-Weil \(L\)-series
zbMATH Keywords: special values
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 937448