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On large value estimates for Dirichlet sums and the density hypothesis for the zeta function
by
Jean Bourgain
Institute for Advanced Study
In the first part of the talk, we discuss a refinement of the Halasz-Montgomery type approach to the distributuion of Dirichlet polynomials. Combined with Jutila's work, it permits the improvement \sigma > [ 25/32] on the known validity range \sigma > [ 11/14] for the density hypothesis N(\sigma, T) < T2(1-\sigma)
The second part of the talk comments on certain
combinatorial aspects of Montgomery's conjectures, such
as the
dimension conjectures for Besicovitch sets in Rd
and
distribution of sequences {n\alpha x } \text mod 1.
Date received: April 4, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caew-64.