On the Nonvanishing of Elliptic Curve L-functions at the Central Point

Abstract

We show that a large number of elliptic curve L-functions do not vanish at the central point, conditionally on the generalized Riemann hypothesis and on a hypothesis on the regular distribution of the root number. Some hypothesis on the root number is necessary because it has not yet been ruled out that the root number is −1 for almost all elliptic curves… (More)

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