University of Lethbridge

In this talk, we present an introduction to p-adic numbers and their appearance in number theory. In particular, we give a proof of Ostrowski's theorem.

Vertex operator algebras (VOAs) as discussed in this talk are graded complex vector spaces with a collection of many bilinear operations satisfying some intricate identities. They first arose in mathematics and physics via the study of string theory...

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.

One version of the Polycirculant Conjecture is that every finite vertex-transitive digraph admits a non-trivial semiregular automorphism. I will give an overview of the status of this conjecture, as well as describe some recent progress with Michael...

We use properties of modular forms to extend the Ramanujan-Mordell formula. Our result yields to formulas for representation numbers by the quadratic form ∑2ai=1x2i+∑2bi=1py2i, for all non-negative integers a,b and for all odd prime p. We obtain this...

We describe a theorem due to Jianya Liu and Yangbo Ye (Pure and Applied Mathematics Quarterly, Volume 3, Number 2, 481-497, 2007) concerning the prime number theorem for automorphic L-functions. We state the theorem and review the strategy of the...

We describe a theorem due to Jianya Liu and Yangbo Ye (Pure and Applied Mathematics Quarterly, Volume 3, Number 2, 481-497, 2007) concerning the prime number theorem for automorphic L-functions. We state the theorem and review the strategy of the...

In 1971, Ruzsa conjectured that if f: N→Z with f(n+k)≡f(n) mod k for every n,k∈N and f(n)=O(θn) with θ

Bertrand's postulate states that there is always a prime in the interval [x,2x] for any x≥1. Applying the prime number theorem, one may further show that there is approximately ∫2xxdtlogt primes in [x,2x] for sufficiently large x. There is a more...

In this talk, I will talk about the fourth moment of quadratic Dirichlet L-functions. Under the generalized Riemann hypothesis, we showed an asymptotic formula for the fourth moment. Unconditionally, we established a precise lower bound.