Random matrix theory and the derivative of the Riemann zeta function
|Title||Random matrix theory and the derivative of the Riemann zeta function |
|Publication Type||Journal Article |
|Year of Publication||2000 |
|Authors||Hughes C, Keating JP, O'Connell N |
|Journal||Proc. R. Soc. Lond. Proc. A |
|Abstract||Random matrix theory is used to model the asymptotics of the discrete moments of the derivative of the Riemann zeta function, $\zeta(s)$, evaluated at the complex zeros $1/2 + i\gamma_n$.
We also discuss the probability distribution of $\ln|\zeta'(1/2+i\gamma_n)|$, proving the central limit theorem for the corresponding random matrix distribution and analysing its large deviations.
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