Low lying zeros of families of L-functions

@article{Iwaniec1999LowLZ,
  title={Low lying zeros of families of L-functions},
  author={Henryk Iwaniec and Wenzhi Luo and Peter Sarnak},
  journal={Publications Math{\'e}matiques de l'Institut des Hautes {\'E}tudes Scientifiques},
  year={1999},
  volume={91},
  pages={55-131}
}
  • H. Iwaniec, W. Luo, P. Sarnak
  • Published 19 January 1999
  • Mathematics
  • Publications Mathématiques de l'Institut des Hautes Études Scientifiques
In Iwaniec-Sarnak [IS] the percentages of nonvanishing of central values of families of GL_2 automorphic L-functions was investigated. In this paper we examine the distribution of zeros which are at or neat s=1/2 (that is the central point) for such families of L-functions. Unlike [IS], most of the results in this paper are conditional, depending on the Generalized Riemann Hypothesis (GRH). It is by no means obvious, but on the other hand not surprising, that this allows us to obtain sharper… 

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