University of Lethbridge

(Please note that this abstract has been reformatted for the web, and some of the original mathematical typesetting may have been lost. Click here [.pdf] for original formatting.) Let n be a positive integer, G be a group and let ν = (ν 1,...,ν n) be...

We shall start by outlining some aspects of the long history of the Artin Conjecture. Then we shall consider a multiplicative subgroup G of Q*. If p is a prime for which the valuation v p(x) = 0 for every x in G, then the group G p ={x (mod p): x is...

I will show how the classical Beurling-Selberg extremal problem in harmonic analysis arises naturally when studying the vertical distribution of the zeros of the Riemann zeta-function and other L-functions. Using this relationship, along with...

An algebra is a vector space with a well-defined multiplication. An operator algebra is an algebra of operators acting on a Hilbert space, typically assumed closed in the norm topology. An easy example of an operator algebra is the algebra M_n(C) of...

The linear independence conjecture asserts that the multisetof positive ordinates of the zeros of automorphic L-functions is linearlyindependent over the eld of rational numbers. This deep conjectureimplies that if 1=2 + i is a zero of the Riemann...

In this talk, we give a brief overview of adelic Hilbert modular forms. Then, we show that the central values of the Rankin-Selberg convolutions, L(g otimes f, s), uniquely determine an adelic Hilbert modular form g, where f varies in a carefully...

Determining the full automorphism group of a graph is a hard problem with a long history. I will discuss some of the major results that involve finding graphs with a given automorphism group. I will then focus on circulant graphs, and describe some...

An automorphism of a Cayley graph that preserves its natural edge-colouring is called colour-preserving. We study groups G with the property that every automorphism on every connected Cayley graph on G is the composition of a left-translation and a...

In 1944, Linnik famously showed unconditionally that the least prime in an arithmetic progression a (mod q) with gcd(a,q)=1 is bounded by q^L for some absolute effective constant L>0, known as “Linnik’s constant”. Many authors have computed explicit...

Very little is known about the distribution of primitive roots of a prime p. Grosswald conjectured that the least primitive root of a prime p is less than the square root of p, minus 2, for all p greater than 409. While this is certainly true for all...