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What is a reference book to understand the relation between the Riemann zeta function and random matrices?

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  • $\begingroup$ Random Matrices - Madan Lal Mehta - Academic Press, Elsevier $\endgroup$
    – A.Neves
    Commented Dec 8, 2023 at 13:21
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    $\begingroup$ If you are an undergraduate, you might look at An Invitation to Modern Number Theory by Miller and Takloo-Bighash $\endgroup$
    – Stopple
    Commented Dec 8, 2023 at 16:19

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There is a substantial literature; for an introduction, you could start with the chapter by Keating and Snaith in the Handbook of Random Matrix Theory. For a more specialized overview, take a look at Recent Perspectives in Random Matrix Theory and Number Theory.

For a selection of research articles on this topic, see the list given by Matthew Watkins (scroll to the bottom of the page).

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