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Uniform distribution of Heegner points

Uniform distribution of Heegner points Invent. math. 148, 1–46 (2002) Digital Object Identifier (DOI) 10.1007/s002220100183 V. Vatsal Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada (e-mail: vatsal@math.ubc.ca) Oblatum 30-X-2000 & 26-VII-2001 Published online: 18 January 2002 –  Springer-Verlag 2002 1 Introduction Let E be a (modular!) elliptic curve over Q, of conductor N.Let K denote an imaginary quadratic field of discriminant D, with ( N, D) = 1. If p is a prime, then there exists a unique Z -extension K / K such that Gal( K/Q) p ∞ acts nontrivially on Gal( K / K).The field K is called the anticyclotomic ∞ ∞ Z -extension of K.Let E( K ) denote the Mordell-Weil group of E over p ∞ K . Then a fundamental conjecture of Mazur [Maz84] predicts that the size of E( K ) is controlled by the prime factorization of N in K . Equivalently, Mazur’s conjecture relates the size of the Mordell-Weil group to the sign in the functional equation of certain L-series. The conjecture was verified by Greenberg, Rohrlich, and Rubin, in what Mazur calls the exceptional case, when E has complex multiplication by K . More generally, they settled the conjecture for certain http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Inventiones mathematicae Springer Journals

Uniform distribution of Heegner points

Inventiones mathematicae , Volume 148 (1) – Apr 1, 2002

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References (1)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0020-9910
eISSN
1432-1297
DOI
10.1007/s002220100183
Publisher site
See Article on Publisher Site

Abstract

Invent. math. 148, 1–46 (2002) Digital Object Identifier (DOI) 10.1007/s002220100183 V. Vatsal Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada (e-mail: vatsal@math.ubc.ca) Oblatum 30-X-2000 & 26-VII-2001 Published online: 18 January 2002 –  Springer-Verlag 2002 1 Introduction Let E be a (modular!) elliptic curve over Q, of conductor N.Let K denote an imaginary quadratic field of discriminant D, with ( N, D) = 1. If p is a prime, then there exists a unique Z -extension K / K such that Gal( K/Q) p ∞ acts nontrivially on Gal( K / K).The field K is called the anticyclotomic ∞ ∞ Z -extension of K.Let E( K ) denote the Mordell-Weil group of E over p ∞ K . Then a fundamental conjecture of Mazur [Maz84] predicts that the size of E( K ) is controlled by the prime factorization of N in K . Equivalently, Mazur’s conjecture relates the size of the Mordell-Weil group to the sign in the functional equation of certain L-series. The conjecture was verified by Greenberg, Rohrlich, and Rubin, in what Mazur calls the exceptional case, when E has complex multiplication by K . More generally, they settled the conjecture for certain

Journal

Inventiones mathematicaeSpringer Journals

Published: Apr 1, 2002

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