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Uniform distribution of Heegner points
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 Zp-extensionExpand
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On the Iwasawa invariants of elliptic curves
Let p be an odd prime. Suppose that E is a modular elliptic curve/Q with good ordinary reduction at p. Let Q_{oo} denote the cyclotomic Z_p-extension of Q. It is conjectured that Sel_E(Q_{oo}) is aExpand
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CM points and quaternion algebras.
This paper provides a proof of a technical result (Corol- lary 2.10 of Theorem 2.9) which is an essential ingredient in our proof of Mazur's conjecture over totally real number fields (3).
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Canonical periods and congruence formulae
The purpose of this article is to show how congruences between the Fourier coefficients of Hecke eigenforms give rise to corresponding congruences between the algebraic parts of the critical valuesExpand
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Ternary Diophantine equations of signature (p, p, 3)
In this paper, we develop machinery to solve ternary Diophantine equations of the shape Axn + Byn = Cz3 for various choices of coefficients (A,B, C). As a byproduct of this, we show, if p is prime,Expand
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Special values of anticyclotomic $L$-functions
The object of this paper is to extend the results and methods of [Vat01], where it was shown how cases of a conjecture of Mazur on the behavior of L-functions in an anticyclotomic Zp-extension couldExpand
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On the local behaviour of ordinary $$-adic representations
In this paper we study the local behaviour of the Galois representations attached to ordinary �-adic forms and ordinary classical cusp forms. In both cases the splitting of the local representationExpand
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Rank-one twists of a certain elliptic curve
The purpose of this note is to give the first known example for a conjecture of Goldfeld on the number of rank-one curves appearing in a family of quadratic twists. We show unconditionally that theExpand
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The goal of this paper is to study two related problems. The first is a certain maximality property of the Shimura subgroup among multiplicative-type subgroups of the Jacobian J0(N ). The second is aExpand
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