44 research outputs found

    Real zeros of quadratic Dirichlet L-functions

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    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

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    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

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    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