Number one in the UK and eighth in the world in the Times Higher Education rankings of universities under 50 years old

Supporter of LMS Good Practice Award

Random matrix theory and the derivative of the Riemann zeta function

Research group:
Number Theory
TitleRandom matrix theory and the derivative of the Riemann zeta function
Publication TypeJournal Article
Year of Publication2000
AuthorsHughes C, Keating JP, O'Connell N
JournalProc. R. Soc. Lond. Proc. A
Volume456
Pagination2611--2627
AbstractRandom 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.
DOI10.1098/rspa.2000.0628
MathRevMR1799857

Tagged | XML | BibTex | Google Scholar

Edited 7 Oct 2009 - 14:37 by ch540

Back to the Top