Publication Date:
2014-11-20
Description:
We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp (2 N ), SO (2 N ) and O – (2 N ). These averages are used to predict the asymptotic formulae for moments of derivatives of L -functions which arise in number theory. Each formula gives the leading constant of the asymptotic in terms of determinants of hypergeometric functions. We find a differential recurrence relation between these determinants that allows the rapid computation of the ( k +1)st constant in terms of the k th and ( k –1)st. This recurrence is reminiscent of a Toda lattice equation arising in the theory of -functions associated with Painlevé differential equations.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
