University of Lethbridge

In his famous '86 paper, Andrews made several conjectures on the function σ(q) of Ramanujan, including that it has coefficients (which count certain partition-theoretic objects) whose sup grows in absolute value, and that it has infinitely many...

It is a classical problem to understand the set of Jacobians of curves among all abelian varieties, i.e., the image of the map Mg→Ag which sends a curve X to its Jacobian JX. In characteristic p, Ag has interesting filtrations, and we can ask how the...

In 1944, Linnik showed that the least prime in an arithmetic progression given by a mod q for (a,q)=1 is at most cq^L for some absolutely computable constants c and L. A lot of work has gone in computing explicit bounds for c and L. The best known...

In 1896, the prime number theorem was established, showing that π(x) ∼ li(x). Perhaps the most widely used estimates in explicit analytic number theory are bounds on |π(x)-li(x)| or the related error term |θ(x)-x|. In this talk we discuss methods one...

TBC

TBC

The prime number theorem (PNT) gives us the density of primes amongst the natural numbers. We can extend this idea to consider whether we have the asymptotic number of primes predicted by the PNT in a given interval. Currently, this has only been...

For an integer k≥3; Δk (x) :=∑n≤xdk(n)-Ress=1 (ζk(s)xs/s), where dk(n) is the k-fold divisor function, and ζ(s) is the Riemann zeta-function. In the 1950's, Tong showed for all large enough X; Δk(x) changes sign at least once in the interval [X, X +...

In 1979, Erdős conjectured that for k≥9, 2k is not the sum of distinct powers of 3. That is, the set of powers of two (which is 2-automatic) and the 3-automatic set consisting of numbers whose ternary expansions omit 2 has finite intersection. In the...

Many results in algebraic graph theory can be viewed as upper bounds on the size of the automorphism group of graphs satisfying various hypotheses. These kinds of results have many applications. For example, Tutte's classical theorem on 3-valent arc...