University of Lethbridge

Let omega(n) denote the number of distinct prime divisors of n. Let W(m) be a random integer chosen uniformly from the set of natural numbers less than or equal to m. Let X(m) be omega(W(m)). The celebrated Erdos-Kac theorem asserts that if the...

Let q≡1(mod4) be a prime power and Fq be the finite field with q elements. Let 1/2σ1 be fixed. We consider D a monic square-free polynomial in Fq[T] and χD the Kronecker symbol associated with D. In this talk, we will discuss the distribution of...

Deep learning lies at the forefront of the artificial intelligence revolution. Stunning successes has been achieved by deep learning for challenging tasks such as image classification. Yet, current deep learning implementations have a tendency to be...

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.

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...

Siegel zeros (or Landau-Siegel zeros) are potential counterexamples to the generalised Riemann hypothesis (for L-functions). Such zeros, if exist, have to be "very close" to 1 over the complex plane. In this talk, we will discuss some results...

The ternary Goldbach problem stated that every odd integer greater than 5 can be written as sums of three primes. This was proved by Vinogradov for all sufficiently large odd integers and completely proved by Helfgott. On the other hand, by using...

L-functions associated with automorphic forms are vast generalizations of Riemann zeta functions and Dirichlet L-functions. Although the theory of L-functions play a fundamental role in number theory, it is still largely conjectural. If π is an...

What happens when you add up the divisors of an integer? This seemingly innocuous question has motivated mathematicians across the ages, from antiquity to the present day. In this talk, we'll survey some conjectures and results on the functions s(n)...

We describe various models of creating communities of mathemati- cal explorers, inspired by our work at Illinois and Washington, and earlier work at Maryland. We will outline how we think any Math department can be the center of a vibrant...