A Hybrid Euler-hadamard Product Formula for the Riemann Zeta Function

@inproceedings{Hughes2005AHE,
title={A Hybrid Euler-hadamard Product Formula for the Riemann Zeta Function},
author={Charles P. Hughes and Jonathan P. Keating},
year={2005}
}

We use a smoothed version of the explicit formula to find an approximation to the Riemann zeta function as a product over its nontrivial zeros multiplied by a product over the primes. We model the first product by characteristic polynomials of random matrices. This provides a statistical model of the zeta function that involves the primes in a natural way. We then employ the model in a heuristic calculation of the moments of the modulus of the zeta function on the critical line. This… CONTINUE READING