University of Lethbridge

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...

In this talk, we will discuss a well-known formula of Ramanujan and its relationship with the partial sums of the Möbius function. Under some conjectures, we analyze a finer structure of the involved terms. It is a joint work with Steven M. Gonek...

Let G be a graph with adjacency matrix A. A continuous quantum walk on G is determined by the complex unitary matrix U(t)=exp(itA), where i2=−1 and t is a real number. Here, G represents a quantum spin network, and its vertices and edges represent...

In 1909, Thue proved that when $F(x,y)$ is an irreducible, homogeneous, polynomial with integer coefficients and degree at least 3, the inequality $\left\| F(x,y) \right\| \leq h$ has finitely many integer-pair solutions for any positive $h$. Because...

Fix $N\geq 1$ and let $L_1, L_2, \ldots, L_N$ be Dirichlet L-functions with distinct, primitive and even Dirichlet characters. We assume that these functions satisfy the same functional equation. Let $F(s)∶= c_1L_1(s)+c_2L_2(s)+\ldots+c_NL_N(s)$ be a...

I will discuss the fourth moment of quadratic Dirichlet L-functions where we prove an asymptotic formula with four main terms unconditionally. Previously, the asymptotic formula was established with the leading main term under generalized Riemann...

I will explain how the Geometric Lemma allows us to classify parabolically induced representations of the p-adic group $G_2$ distinguished by $SO_4$. In particular, I will describe a new approach, in progress, where we use the structure of the p-adic...

The topic on the distribution of sequences saw its light with the seminal paper of Weyl. While the classical notion of equidistribution modulo one addresses the “global” behaviour of the fractional parts of a sequence, quantities such as k-point...