71 research outputs found
The cubic moment of central values of automorphic L-functions
The authors study the central values of L-functions in certain families; in
particular they bound the sum of the cubes of these values.Contents:Comment: 42 pages, published versio
Low lying zeros of families of L-functions
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 results on nonvanishing.Comment: Abstract added in migration (from introduction
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