%0 Journal Article
%T Zero repulsion in families of elliptic curve L-functions and an observation of S. J. Miller
%A Simon Marshall
%J Mathematics
%D 2011
%I arXiv
%R 10.1112/blms/bds063
%X 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.
%U http://arxiv.org/abs/1109.0224v3