University of Lethbridge

In 1770 Euler observed that 3 3 + 4 3 + 5 3 = 6 3 and asked if there was another perfect power that equals the sum of consecutive cubes. This captivated the attention of many important mathematicians, such as Cunningham, Catalan, Genocchi and Lucas...

We will explore how a Fourier optimization framework may be used to study two classical problems in number theory involving Dirichlet characters: The problem of estimating the least character non-residue; and the problem of estimating the least prime...

I am going to discuss various results on moments of symmetric square L-functions and some of their applications. I will mainly focus on a recent result of R. Khan and M. Young and our improvement of it. Khan and Young proved a mean Lindelöf estimate...

Previously we found certain convolution sums of divisor functions arising from physics yield Fourier coefficients of modular forms. In this talk we will discuss the limitations of the current proof of these formulas. We will also explore the...

The Polya group Po(K) of a Galois number field K coincides with the subgroup of the ideal class group Cl(K) of K consisting of all strongly ambiguous ideal classes. We prove that there are only finitely many imaginary abelian number fields K whose...

There is a beautiful connection between the prime numbers and the zeros of Riemann zeta- function in the complex plane, and understanding the distribution of these zeros can lead to remarkable consequences in our understanding of the primes. A famous...

We provide a detailed study on effective versions of the celebrated Bilu's equidistribution theorem for Galois orbits of sequences of points of small height in the N-dimensional algebraic torus, identifying the qualitative dependence of the...

I will discuss recent work with Chantal David, Alexander Dunn, and Joshua Stucky, in which we prove that a positive proportion of Hecke L-functions associated to the cubic residue symbol modulo square-free Eisenstein integers do not vanish at the...

Let $d>k$ be positive integers. Motivated by an earlier result of Bugeaud and Nguyen, we let $E_{k,d}$ be the set of $(c_1,\ldots,c_k)\in\mathbb{R}_{\geq 0}^k$ such that $\vert\alpha_0\vert\vert\alpha_1\vert^{c_1}\cdots\vert\alpha_k\vert^{c_k}\geq 1$...

Bounds on the logarithmic derivative and the reciprocal of the Riemann zeta function are studied as they have a wide range of applications, such as computing bounds for Mertens function. In this talk, we are mainly concerned with explicit bounds...