University of Lethbridge

We will discuss a graph that encodes the divisibility properties of integers by primes. We prove that this graph has a strong local expander property almost everywhere. We then obtain several consequences in number theory, beyond the traditional...

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The prime number theorem (PNT) gives us the density of primes amongst the natural numbers. We can extend this idea to consider whether we have the asymptotic number of primes predicted by the PNT in a given interval. Currently, this has only been...

For an integer k≥3; Δk (x) :=∑n≤xdk(n)-Ress=1 (ζk(s)xs/s), where dk(n) is the k-fold divisor function, and ζ(s) is the Riemann zeta-function. In the 1950's, Tong showed for all large enough X; Δk(x) changes sign at least once in the interval [X, X +...

In 1979, Erdős conjectured that for k≥9, 2k is not the sum of distinct powers of 3. That is, the set of powers of two (which is 2-automatic) and the 3-automatic set consisting of numbers whose ternary expansions omit 2 has finite intersection. In the...

Many results in algebraic graph theory can be viewed as upper bounds on the size of the automorphism group of graphs satisfying various hypotheses. These kinds of results have many applications. For example, Tutte's classical theorem on 3-valent arc...

In this talk, I will discuss my on-going joint work with Xiannan Li on an unconditional asymptotic formula for the eighth moment of Γ1(q) L-functions, which are associated with eigenforms for the congruence subgroups Γ1(q). Similar to a large family...

Math Circles are the improvisational comedy of mathematics: you start with a script, and then you say “yes, and...” to all questions and queries, building an atmosphere of exploration and discovery that builds enthusiasm for mathematics. They work at...

Join us for the ULethbridge Math Fair Saturday, Feb 8 2020| 10AM - 2PM | SA7330 Outreach in Science Commons Fun math activities for students in grades K-12 * Platonic Solids * Math Games * Mathematical Colouring