Twisted moments of characteristic polynomials of random matrices in the unitary group
Abstract
Abstract Recently, Conrey and Keating devised a heuristic for predicting asymptotic formulas for moments of the Riemann zeta‐function . Their approach indicates how lower twisted moments of may be used to evaluate higher moments. In this paper, we present a rigorous random matrix theory analogue of their heuristic. To do this, we develop a notion of “twisted moments” of characteristic polynomials of matrices in the unitary group , and we prove several identities involving Schur polynomials. Our results may be viewed as a proof of concept for the heuristic for .
Fields of Study & Subjects
Random Matrices and Applications
Advanced Algebra and Geometry
advanced mathematical theories
Publication details
- Journal / source
- Proceedings of the London Mathematical Society
- Volume
- 133
- Issue
- 2
- Publication date
- 1 August 2026
- Language
- EN