## Abstract

We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O - (2N). 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 kth and (k-1)st. This recurrence is reminiscent of a Toda lattice equation arising in the theory of π-functions associated with Painlevé differential equations.

Original language | English (US) |
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Pages (from-to) | 1111-1125 |

Number of pages | 15 |

Journal | Quarterly Journal of Mathematics |

Volume | 65 |

Issue number | 4 |

DOIs | |

State | Published - Nov 21 2013 |