Brian Conrey

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math-ph2024

Moments of the derivative of the characteristic polynomial of unitary matrices

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

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

math.NT2024

Character Sums and the Riemann Hypothesis

Brian Conrey

We prove that an innocent looking inequality implies the Riemann Hypothesis and show a way to approach this inequality through sums of Legendre symbols.