University of Lethbridge

Dirichlet's theorem on arithmetic progressions states that for any (a,q)=1, there are infinitely many primes congruent to a modulo q. Such a theorem together with Euler's earlier work on the infinitude of primes represents the beginning of the study...

Quadratic fields have been studied since the time of Gauss, and in modern times have been used in applications such as integer factorization and public-key cryptography. In this talk, we will give a brief overview of some applications and...

The classic theorem of Chebotarev tells us that for any Galois extension L/K of degree n the proportion of primes of K, whose Frobenius conjugacy class is a given conjugacy class of the Galois group is proportional to the size of that conjugacy class...

The relationship between independence number, chromatic number, clique number, clique cover number and their fractional analogues is well-established for perfect graphs. Here, we study the clique k-cover number cck(G) and the fractional clique k...

In the past twenty years there has been a flurry of activity in the study of mean values of L-functions. This was precipitated by groundbreaking work of Keating and Snaith in which they modelled these mean values by random matrix theory. In this talk...

A Dirichlet polynomial is a function of the form $A(t)=\sum_{n \le N} a_n n^{-it}$ where $a_n$ is a complex sequence, $N \in \mathbb{N}$, and $t \in \mathbb{R}$. For $T \ge 1$, the mean values$$\int_{0}^{T} |A(t)|^2 \, dt$$play an important role in...

In this talk I will discuss joint work with Clifton Cunningham, Ahamed Moussaui, James Mracek and Bin Xu. I will begin by giving a brief overview of the (conjectural) Langlands Correspondence, focusing in particular on Vogan's geometric reformulation...

Reduced ideals of a number field F have inverses of small norms and they form a finite and regularly distributed set in the infrastructure of F. Therefore, they can be used to compute the regulator and the class number of a number field. One usually...

A Dirichlet polynomial is a function of the form $A(t)=\sum_{n \le N} a_n n^{-it}$ where $a_n$ is a complex sequence, $N \in \mathbb{N}$, and $t \in \mathbb{R}$. For $T \ge 1$, the mean values $$\int_{0}^{T} |A(t)|^2 \, dt$$ play an important role in...

Description (in plain text format): The modularity theorem tells us that for every elliptic curve E over the field Q of rational numbers, there is a modular form f such that the L-function L(s,f) for f coincides with the L-function L(s,rho) for the...