We show in this paper that after proper scalings, the characteristic polynomial of a random
unitary matrix converges to a random analytic function whose zeros, which are on the real …

The complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann-
function,. Thus, if the Riemann hypothesis (RH) is true for the zeta-function, then it is true for …

Assuming the Riemann hypothesis and a hypothesis on small gaps between zeta zeros (see
equation (ES 2K) below for a precise definition), we prove a conjecture of Bailey, Bettin …

We prove asymptotics for real moments of the logarithmic derivative of characteristic
polynomials evaluated at $1-\frac {a}{N} $ in unitary, even orthogonal, and symplectic …

We study moments of the logarithmic derivative of characteristic polynomials of orthogonal
and symplectic random matrices. In particular, we compute the asymptotics for large matrix …

We investigate the distribution of the logarithmic derivative of the Riemann zeta-function on
the line ℜ (s)= σ, where σ lies in a certain range near the critical line σ= ½. For such σ, we …

A one-parameter family of point processes describing the distribution of the critical points of
the characteristic polynomial of large random Hermitian matrices on the scale of mean …

We estimate the covariance in counts of almost-primes in, weighted by higher-order von
Mangoldt functions. The answer takes a pleasant algebraic form. This generalizes recent …

In the present paper, we show that, for every δ> 0, the function (log⁡ L (s))(m), where m∈
N∪{0} and L (s):=∑ n= 1∞ a (n) n− s is an element of the Selberg class S, takes any value …

The study of statistical properties of characteristic polynomials of random matrices from the
classical compact ensembles is rich and diverse in applications. In this thesis, we study a …