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.

38 pages. v3: Improved and expanded exposition, error corrections. To appear in the Proceedings of the London Mathematical Society

References in corpus (3)

• 1- and 2-Level Densities for Rational Families of Elliptic Curves: Evidence for the Underlying Group Symmetries
• Lower-Order Terms of the 1-Level Density of Families of Elliptic Curves
• Applications of the L-functions ratios conjectures

Cited by in corpus (1)

• Moments of the critical values of families of elliptic curves, with applications