Form an n × n matrix by drawing entries independently from {±1} (or another fixed nontrivial finitely supported distribution in Z) and let φ be the characteristic polynomial. We show, conditionally on the extended Riemann hypothesis, that with high probability φ is irreducible and Gal(φ) ≥ An.
article
entry
https://scigraph.springernature.com/explorer/license/
random matrices
n matrix
2022-03-14
491-527
characteristic polynomial
2022-12-01T06:44
The Characteristic Polynomial of a Random Matrix
polynomials
true
matrix
An
Riemann hypothesis
hypothesis
https://doi.org/10.1007/s00493-020-4657-0
2022-03-14
articles
Extended Riemann Hypothesis
Mathematical Sciences
Springer Nature - SN SciGraph project
doi
10.1007/s00493-020-4657-0
Eberhard
Sean
pub.1146254930
dimensions_id
Pure Mathematics
1439-6912
0209-9683
Springer Nature
Combinatorica
4
42
Centre for Mathematical Sciences, Wilberforce Road, CB3 0WB, Cambridge, UK
Centre for Mathematical Sciences, Wilberforce Road, CB3 0WB, Cambridge, UK