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Publications Influence

Uniform distribution of Heegner points

- V. Vatsal
- Mathematics
- 1 April 2002

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-extension… Expand

119 13- PDF

L -functions and Galois Representations: Nontriviality of Rankin-Selberg L -functions and CM points

74 12- PDF

On the Iwasawa invariants of elliptic curves

- Ralph Greenberg, V. Vatsal
- Mathematics
- 19 June 1999

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 a… Expand

121 12- PDF

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).

51 11- PDF

Canonical periods and congruence formulae

- V. Vatsal
- Mathematics
- 1 June 1999

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 values… Expand

91 10- PDF

Ternary Diophantine equations of signature (p, p, 3)

- M. Bennett, V. Vatsal, S. Yazdani
- Mathematics
- 1 November 2004

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

42 5- PDF

Special values of anticyclotomic $L$-functions

- V. Vatsal
- Mathematics
- 1 March 2003

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 could… Expand

85 5- PDF

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 representation… Expand

40 5- PDF

Rank-one twists of a certain elliptic curve

- V. Vatsal
- Mathematics
- 1 August 1998

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 the… Expand

35 4

MULTIPLICATIVE SUBGROUPS OF J 0 ( N ) AND APPLICATIONS TO ELLIPTIC CURVES

- V. Vatsal
- Mathematics
- 1 April 2005

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 a… Expand

29 3- PDF