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arXiv · 1109.0224

Zero repulsion in families of elliptic curve L-functions and an observation of S. J. Miller

Simon Marshall
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Abstract

We provide a theoretical explanation for an observation of S. J. Miller that if L(s,E) is an elliptic curve L-function for which L(1/2, E) is nonzero, then the lowest lying zero of L(s,E) exhibits a repulsion from the critical point which is not explained by the standard Katz-Sarnak heuristics. We establish a similar result in the case of first-order vanishing.

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Simon Marshall. 2011-10-20. Zero repulsion in families of elliptic curve L-functions and an observation of S. J. Miller. https://doi.org/10.1112/blms%2Fbds063

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