University of Lethbridge

For any finite group G, a natural question to ask is the order of the smallest possible automorphism group for a Cayley graph on G. A particular Cayley graph whose automorphism group has this order is referred to as an MRR (Most Rigid Representation)...

The study of the asymptotic behaviour of the summatory function of the number of divisors of shifted primes was initiated by Titchmarsh, who used the generalised Riemann hypothesis to establish a main term and remainder for the sum of tau(p-a) for p...

Well, it's not really a construction yet -- it's more like a template for constructions. It's a way to take many copies of one tetravalent graph B, the 'base graph', and identify each edge-midpoint with one other according to another graph C, the...

In this talk we report on some research projects from summer 2017 supported by NSERC-USRA. In the first part of the project, we surveyed all existing explicit results from the past 60 years on prime counting functions, with a special focus on theta(x...

Let $\phi(n)$ be Euler's totient function and let $q$ and $a$ be fixed coprime natural numbers. Denote by $S_{q,a}$ the set of natural numbers whose prime divisors are all congruent to $a$ modulo $q$. We can establish \[\limsup_{n \in S_{q,a}} \frac...

Given a field K, a K-valued sequence is said to satisfy a linear recurrence if the n-th term can be expressed as a fixed K-linear combination of the preceding d terms for some d. The sequence of Fibonacci numbers is a famous example of such a...

A packing of translates of a convex domain in the Euclidean plane is said to be totally separable if any two packing elements can be separated by a line disjoint from the interior of every packing element. This notion was introduced by G. Fejes Toth...

It is well known that the prime numbers are equidistributed in arithmetic progression. Such a phenomenon is also observed more generally for a class of multiplicative functions. We derive some variants of such results and give an application to...

I will discuss the connections between metric Diophantine approximation and the construction of measures whose Fourier transform decays as fast as possible (relative to the Hausdorff dimension of the support of the measure). Concepts like Diophantine...

Let K/k be a Galois extension of number fields with Galois group G, and let rho be a non-trivial irreducible representation of G of dimension n. The Artin holomorphy conjecture asserts that the Artin L-function attached to rho extends to an entire...