University of Lethbridge

A Dirichlet character over Fq(t) corresponds to a curve over Fq. Using this connection to geometry, we construct families of characters whose L-functions vanish (resp. does not vanish) at the central point. The existence of infinitely many vanishing...

Let K/k be a finite Galois extension. We define a principal version of the Chebotarev density theorem which represents the density of prime ideals of k that factor into a product of principal prime ideals in K. We find explicit equations to express...

We improve the best known to date result of Dress-Iwaniec-Tenenbaum, getting (log x)^2 instead of (log x)^(5/2). We use a weighted form of Vaughan's identity, allowing a smooth truncation inside the procedure, and an estimate due to Barban-Vehov and...

Kummer theory is a classical theory about radical extensions of fields in the case where suitable roots of unity are present in the base field. Motivated by problems close to Artin's primitive root conjecture, we have investigated the degree of...

In this talk, I will present a recent joint work with Yoonbok Lee, where we investigate the number of zeros of linear combinations of $L$-functions in the vicinity of the critical line. More precisely, we let $L_1, \dots, L_J$ be distinct primitive...

I will talk about recent work towards a conjecture of Gonek regarding negative shifted moments of the Riemann zeta-function. I will explain how to obtain asymptotic formulas when the shift in the Riemann zeta function is big enough, and how we can...

The Hurwitz zeta function $\zeta(s, \alpha)$ is a shifted integer analogue of the Riemann zeta function which shares many of its properties, but is not an ”L-function” under any reasonable definition of the word. We will first review the basics of...

The quality of the triplet $(a,b,c)$, where $\gcd(a,b,c) = 1$, satisfying $a + b = c$ is defined as $$ q(a,b,c) = \frac{\max\{\log |a|, \log |b|, \log |c|\}}{\log \mathrm{rad}(|abc|)}, $$ where $\mathrm{rad}(|abc|)$ is the product of distinct prime...

The blow up of the anticanonical base point on X, a del Pezzo surface of degree 1, gives rise to a rational elliptic surface E with only irreducible fibers. The sections of minimal height of E are in correspondence with the 240 exceptional curves on...

The Fibonacci sequence \(F(n) : (n\geq 0) is the binary recurrence sequence defined by $$ F(0) = F(1) = 1 \qquad \mbox{and} \\ F(n+2) = F(n+1) + F(n) \qquad \forall n \geq 0. $$ There is a broad literature on the Diophantine equations involving the...