The characteristic polynomial of a random matrix

Sean Eberhard

doi:10.1007/s00493-020-4657-0

The characteristic polynomial of a random matrix

Sean Eberhard^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

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) ≥ A_n.

Original language	English
Pages (from-to)	491-527
Number of pages	37
Journal	Combinatorica
Volume	42
Issue number	4
Early online date	14 Mar 2022
DOIs	https://doi.org/10.1007/s00493-020-4657-0
Publication status	Published - Aug 2022
Externally published	Yes

Bibliographical note

Funding Information:
The author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 803711).

Publisher Copyright:
© 2022, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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Cite this

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abstract = "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.",

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The characteristic polynomial of a random matrix

Abstract

Bibliographical note

ASJC Scopus subject areas

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