Altuğ, SA;
Bettin, S;
Petrow, I;
Rishikesh;
Whitehead, I;
(2014)
A recursion formula for moments of derivatives of random matrix polynomials.
The Quarterly Journal of Mathematics
, 65
(4)
pp. 1111-1125.
10.1093/qmath/hat054.
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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 τ-functions associated with Painlevé differential equations.
| Type: | Article |
|---|---|
| Title: | A recursion formula for moments of derivatives of random matrix polynomials |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/qmath/hat054 |
| Publisher version: | https://doi.org/10.1093/qmath/hat054 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10084832 |
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