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LINEAR INDEPENDENCE OF HECKE OPERATORS IN THE HOMOLOGY OF X0(N)

Published online by Cambridge University Press:  01 April 2000

JEFFREY M. VANDERKAM
JEFFREY M. VANDERKAM
Affiliation:
Department of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA; vanderkm@idaccr.org
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Abstract

In Merel's recent proof [7] of the uniform boundedness conjecture for the torsion of elliptic curves over number fields, a key step is to show that for sufficiently large primes N, the Hecke operators T1, T2, …, TD are linearly independent in their actions on the cycle e from 0 to i∞ in H1(X0(N) (C), Q). In particular, he shows independence when max(D8, 400D4) < N/(log N)4. In this paper we use analytic techniques to show that one can choose D considerably larger than this, provided that N is large.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 349 - 358
Copyright
The London Mathematical Society 2000

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