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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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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.