University of Lethbridge

In this talk we report on some research projects from summer 2017 supported by NSERC-USRA. In the first part of the project, we surveyed all existing explicit results from the past 60 years on prime counting functions, with a special focus on theta(x...

It is well known that the prime numbers are equidistributed in arithmetic progression. Such a phenomenon is also observed more generally for a class of multiplicative functions. We derive some variants of such results and give an application to...

A packing of translates of a convex domain in the Euclidean plane is said to be totally separable if any two packing elements can be separated by a line disjoint from the interior of every packing element. This notion was introduced by G. Fejes Toth...

Given a field K, a K-valued sequence is said to satisfy a linear recurrence if the n-th term can be expressed as a fixed K-linear combination of the preceding d terms for some d. The sequence of Fibonacci numbers is a famous example of such a...

Let $\phi(n)$ be Euler's totient function and let $q$ and $a$ be fixed coprime natural numbers. Denote by $S_{q,a}$ the set of natural numbers whose prime divisors are all congruent to $a$ modulo $q$. We can establish \[\limsup_{n \in S_{q,a}} \frac...

A "Strongly Regular Graph", SRG(?,k,lambda,mu), is a k-regular graph with v vertices such that every two adjacent vertices have lambda common neighbors, and every two non-adjacent vertices have mu common neighbors. Let M be any power of 2, and let M'...

Description (in plain text format): The modularity theorem tells us that for every elliptic curve E over the field Q of rational numbers, there is a modular form f such that the L-function L(s,f) for f coincides with the L-function L(s,rho) for the...

Please bring your favourite unsolved 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. Everyone is welcome.

A Dirichlet polynomial is a function of the form $A(t)=\sum_{n \le N} a_n n^{-it}$ where $a_n$ is a complex sequence, $N \in \mathbb{N}$, and $t \in \mathbb{R}$. For $T \ge 1$, the mean values$$\int_{0}^{T} |A(t)|^2 \, dt$$play an important role in...

A Dirichlet polynomial is a function of the form $A(t)=\sum_{n \le N} a_n n^{-it}$ where $a_n$ is a complex sequence, $N \in \mathbb{N}$, and $t \in \mathbb{R}$. For $T \ge 1$, the mean values $$\int_{0}^{T} |A(t)|^2 \, dt$$ play an important role in...