University of Lethbridge

We consider a variant of a problem first introduced by Hughes and Rudnick (2003) and generalized by Bernard (2015) concerning conditional bounds for small first zeros in a family of L-functions. Here we seek to estimate the size of the smallest...

The values of Dirichlet L-functions at s=1 have long attracted considerable attention due to their deep algebraic and geometric significance. In contrast, the logarithmic derivatives of Dirichlet L-functions at s=1, which play a key role in the study...

Deuring-Heilbronnn phenomenon, quantitatively established by Linnik in 1944, describes how the existence of a Landau-Siegel zero, which is real and near s=1, affects the location of the rest of the zeros of the Dirichlet L-functions to the same...

A bijection f of a metric space is "distance-permuting" if the distance from f(x) to f(y) depends only on the distance from x to y. For example, it it is known that every distance-permuting bijection of the real line is the composition of an isometry...

It has been known since the 80s, thanks to Conrey and Ghosh, that the average of the square of the Riemann zeta function, summed over the extreme points of zeta up to a height $T$, is $\frac{1}{2} (e^2-5) \log T$ as $T \rightarrow \infty$. This...

I will start with a survey on sums of random multiplicative functions, focusing on distributional questions and almost sure upper bounds and $\Omega$-results. In this context, I will describe previous work with Jake Chinis on a central limit theorem...

The higher-order Titchmarsh problem concerns the correlation between higher divisor functions and primes. In this talk, I will explain how to derive an asymptotic formula for this correlation in appropriate ranges, assuming the existence of a "strong...

Let $\rm{ord}_p(a)$ be the order of $a$ in $( \mathbb{Z} / p \mathbb{Z} )^*$. In 1927, Artin conjectured that the set of primes $p$ for which an integer $a\neq -1,\square$ is a primitive root (i.e. $\rm{ord}_p(a)=p-1$) has a positive asymptotic...

Even though Euler products of L-functions are generally valid only to the right of the critical strip, there is a strong sense in which they should persist even inside the critical strip. Indeed, the behaviour of Euler products inside the critical...

TBA