## Research Abstracts Online

January 2009 - March 2010

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### University of Minnesota Twin Cities

Institute of Technology

School of Mathematics

# PI: Andrew M. Odlyzko

### Statistical Analysis of Values of the Riemann Zeta Function

There is active research going on around the world on the (so far largely speculative) connection between the Riemann zeta function from pure number theory and random matrices that arise in quantum chaos studies. In particular, analogies have been drawn between the behavior of the zeta function on the critical line and some matrix models that have led to new conjectures, not approachable (as far anyone knows) from number theoretic viewpoints, about the asymptotics of the moments of the zeta function on the critical line.

The aim of this project is to obtain numerical data to check these conjectures, as well as some other conjectures about the "envelope-like” behavior of values of the zeta function. These researchers have a database of over 20 billion zeros of the Riemann zeta functions and related values, most near zero number 1023. They have developed codes for efficient computation of moments of the zeta function from this data.

In previous periods, the codes were tested and then run to obtain most of the values of moments of the zeta function that are needed. What remains is to analyze the data and write up the results.

### Group Member

Ghaith Hiary, Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada