Random matrix theory and discrete moments of the Riemann zeta function

Details Random matrix theory and discrete moments of the Riemann zeta function Random matrix theory and discrete moments of the Riemann zeta function

2002-07-25

arxiv.org/abs/math/0207236v2

Mathematics

Number Theory

Replacement corrects slight typos. To be published in J. Phys. A, special issue in Random Matrix Theory

Scientific paper

10.1088/0305-4470/36/12/303

We calculate the discrete moments of the characteristic polynomial of a
random unitary matrix, evaluated a small distance away from an eigenangle. Such
results allow us to make conjectures about similar moments for the Riemann zeta
function, and provide a uniform approach to understanding moments of the zeta
function and its derivative.

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