University of Lethbridge

The Riemann Hypothesis predicts that all zeros of the Riemann zeta function are located on the line Re(s) = 1/2. Also, we have that the number of zeros with imaginary parts located between T and 2T is approximately (T log T)/(2pi). Therefore the...

Let h be a natural number and f an arithmetic function. The autocorrelation of f is the sum (over all n less than some x) of the product f(n) f(n+h). Such sums play an important role in analytic number theory. For instance, consider the classical...

In this talk, we will discuss order convergence and unbounded order convergence (uo-convergence) on vector lattices. In many classical function spaces, uo-convergence agrees with almost everywhere convergence. Thus, uo-convergence may be viewed as a...

For a prime p, let n(p) be the number of solutions (x, y) of y^2 = x^3 + ax + b over the finite field F_p and let a(p) = p - n(p). In 1976, Serge Lang and Hale Trotter formulated a conjecture regarding the distribution of primes p for which a(p) = A...

For a field F and a quadratic form Q defined on an n-dimensional vector space V over F, let GQ, called the quadratic graph associated to Q, be the graph with the vertex set V where vertices v, w in V form an edge if and only if Q(v-w) = 1. Quadratic...

A Cayley graph Cay(G;S) on a group G with connection set S (closed under inverses) is the graph whose vertices are the elements of G, with g adjacent to h if and only if h is in gS. If we assign a colour c(s) to each s in S so that the inverse of s...

Please bring your favourite (math) problems. Anyone with a problem to share will be given about 5 minutes to present it. We will also choose most of the speakers for the rest of the semester.

The Lang-Trotter Conjecture for primitive points predicts an expression for the density of primes p for which a fixed rational point (not torsion) of a fixed elliptic curve defined on the rational numbers is a generator of the curve reduced modulo p...

(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...