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A new statistical model of the Riemann zeta function

Thursday 15th July 2004 - 16:00 to 16:45
INI Seminar Room 1
Session Title: 
Matrix Ensembles and L-Functions

The characteristic polynomial models of the Riemann zeta function and other L-functions have allowed us to predict answers to a variety of questions previously considered intractable. However, these powerful models have contained no arithmetical information, which generally has to be introduced in an ad hoc manner. I will present a new model for the zeta function developed with C. Hughes and J. Keating that overcomes this difficulty. I will illustrate its use by calculating moments of the Riemann zeta function and estimating the maximal order of the zeta function on the critical line.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons