44 research outputs found
Real zeros of quadratic Dirichlet L-functions
We show that for a positive proportion of real primitive Dirichlet characters
chi, the associated Dirichlet L-function L(s,chi) has no zeros on the positive
real axis. Prior to this it was not known whether or not there were infinitely
many L-functions (from any family) with no positive real zeros.Comment: 38 page
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
High moments of the Riemann zeta-function
The authors describe a general approach which, in principal, should produce
the correct (conjectural) formula for every even integer moment of the Riemann
zeta function. They carry it out for the sixth and eigth powers; in the case of
sixth powers this leads to the formula conjectured by Conrey and Ghosh, and in
the case of eighth powers is new.Comment: Abstract added in migratio