Joint moments of derivatives of characteristic polynomials of random symplectic and orthogonal matrices
dc.contributor.author | Andrade, JC | |
dc.contributor.author | Best, CG | |
dc.date.accessioned | 2024-05-08T09:43:10Z | |
dc.date.issued | 2024-05-08 | |
dc.date.updated | 2024-05-07T14:19:32Z | |
dc.description.abstract | We investigate the joint moments of derivatives of characteristic polynomi als over the unitary symplectic group Sp(2N) and the orthogonal ensembles SO(2N) and O −(2N). We prove asymptotic formulae for the joint moments of the n1th and n2th derivatives of the characteristic polynomials for all three matrix ensembles. Our results give two explicit formulae for each of the leading order coefficients, one in terms of determinants of hypergeometric functions and the other as combinatorial sums over partitions. We use our results to put forward conjectures on the joint moments of derivatives of L-functions with symplectic and orthogonal symmetry. | en_GB |
dc.description.sponsorship | Leverhulme Trust | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
dc.identifier.doi | https://doi.org/10.1088/1751-8121/ad4075 | |
dc.identifier.grantnumber | RPG-2017-320 | en_GB |
dc.identifier.grantnumber | EP/V520317/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/135910 | |
dc.identifier | ORCID: 0000-0002-3431-6623 (Andrade, Julio) | |
dc.language.iso | en | en_GB |
dc.publisher | IOP Publishing | en_GB |
dc.rights | © 2024 The Author(s). Published by IOP Publishing Ltd. Open access. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. | en_GB |
dc.subject | random matrix theory | en_GB |
dc.subject | joint moments | en_GB |
dc.subject | characteristic polynomials | en_GB |
dc.subject | random symplectic matrices | en_GB |
dc.subject | random orthogonal matrices | en_GB |
dc.subject | Riemann zeta function | en_GB |
dc.subject | L-functions | en_GB |
dc.title | Joint moments of derivatives of characteristic polynomials of random symplectic and orthogonal matrices | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2024-05-08T09:43:10Z | |
dc.identifier.issn | 1751-8113 | |
dc.description | This is the final version. Available on open access from IOP Publishing via the DOI in this record | en_GB |
dc.description | Data availability statement: No new data were created or analysed in this study. | en_GB |
dc.identifier.eissn | 1751-8121 | |
dc.identifier.journal | Journal of Physics A: Mathematical and Theoretical | en_GB |
dc.relation.ispartof | Journal of Physics A: Mathematical and Theoretical | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
dcterms.dateAccepted | 2024-04-18 | |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2024-05-08 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2024-05-08T09:38:28Z | |
refterms.versionFCD | VoR | |
refterms.dateFOA | 2024-05-08T09:43:21Z | |
refterms.panel | B | en_GB |
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Except where otherwise noted, this item's licence is described as © 2024 The Author(s). Published by IOP Publishing Ltd. Open access. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.