N. Snaith

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math-ph2025

Moments of characteristic polynomials and their derivatives for $S O (2 N)$ and $U S p (2 N)$ and their application to one-level density in families of elliptic curve $L$ -functions

I. A. Cooper, N. C. Snaith

Using the ratios theorems, we calculate the leading order terms in $N$ for the following averages of the characteristic polynomial and its derivative: $\left< \left|Î_A(1 )\right|…

math-ph2025

Moments of the derivative of the characteristic polynomial of unitary matrices

Emilia Alvarez, Brian Conrey, Michael O. Rubinstein +1

Let $I^_{X} (s) = det (I - s X^{†})$ be the characteristic polynomial of a Haar distributed unitary matrix $X$ . It is believed that the distribution of values of $I^_{X} (s)$ model the…

math-ph2024

Unitary $n$ -correlations with restricted support in random matrix theory

Patrik Demjan, N. C. Snaith

We consider the $n$ -correlation of eigenvalues of random unitary matrices in the alternative form that is not the tidy determinant common in random matrix theory, but rather the ex…

Moments of characteristic polynomials and their derivatives for SO(2N) and USp(2N) and their application to one-level density in families of elliptic curve L-functions

Moments of the derivative of the characteristic polynomial of unitary matrices

Unitary n-correlations with restricted support in random matrix theory

Moments of characteristic polynomials and their derivatives for $S O (2 N)$ and $U S p (2 N)$ and their application to one-level density in families of elliptic curve $L$ -functions

Unitary $n$ -correlations with restricted support in random matrix theory