University of Lethbridge

We establish the fourth moments of the real and imaginary parts of the Riemann zeta-function, as well as the fourth power mean value of Hardy's Z-function at the Gram points. We also study two weak versions of Gram's law. We show that those weak Gram...

In this talk we will discuss the behaviour of the Riemann zeta on the critical line, and in particular, its correlations in various ranges. We will prove a new result for correlations of squares, where shifts may be up to size T3/2-ε. We will also...

The least quadratic non-residue has been a central problem in number theory for centuries. The average least quadratic non-residue was explored by Erdős in the 1960s, and many extensions of this problem such as to the average least character non...

In this talk, we will study the first and second twisted moments of some Rankin-Selberg convolution L-functions of an automorphic form of prime power level. Our first moment result can be used to prove that automorphic forms of suitable weight and...

Subconvexity problems have maintained extreme interest in analytic number theory for decades. Critical barriers such as the convexity, Burgess, and Weyl bounds hold particular interest because one usually needs to drastically adjust the analytic...

There are two ways to compute moments in families of L-functions: one uses the approximation by Dirichlet polynomials, and the other is based on multiple Dirichlet series. We will introduce the two methods to study the family of real Dirichlet L...

A directed variant of the famous Oberwolfach problem, the directed Oberwolfach problem considers the following scenario. Given n people seated at t round tables of size m1,m2…,mt, respectively, such that m1+m2+⋯+mt=n, does there exist a set of n−1...

We study sums of the form ∑n≤x f(n) n⁻ⁱʸ, where f is an arithmetic function, and we establish an equivalence between the Riemann Hypothesis and estimates on these sums. In this talk, we will explore examples of such sums with specific arithmetic...

We will present a matching upper and lower bound for the right tail probability of the maximum of a random model of the Riemann zeta function over short intervals. In particular, we show that the right tail interpolates between that of log-correlated...

In 1973, assuming the Riemann hypothesis (RH), Montgomery studied the vertical distribution of zeta zeros, and conjectured that they behave like the eigenvalues of some random matrices. We will discuss some models for zeta zeros � starting from the...