University of Lethbridge

The behavior of quadratic twists of modular L-functions at the critical point is related both to coefficients of half integer weight modular forms and data on elliptic curves. Here we describe a proof of an asymptotic for the second moment of this...

The blow up of the anticanonical base point on X, a del Pezzo surface of degree 1, gives rise to a rational elliptic surface E with only irreducible fibers. The sections of minimal height of E are in correspondence with the 240 exceptional curves on...

In the finite-dimensional situation, Lie's third theorem provides a correspondence between Lie groups and Lie algebras. Going from the latter to the former is the more complicated construction, requiring a suitable representation, and taking...

We compute extreme values of the Riemann Zeta function at the critical points of the zeta function in the critical strip. i.e. the points where ζ′(s)=0 and Rs1. We show that the values taken by the zeta function at these points are very similar to...

In the past century, the studies of moments of L-functions have been important in number theory and are well-motivated by a variety of arithmetic applications. This talk will begin with two problems in elementary number theory, followed by a survey...

In this talk we will present a method to study the Galois group of certain polynomials defined over ℚ. Our approach is similar in spirit to some previous work of F. Hajir, who studied, more than a decade ago, the generalized Laguerre polynomials...

We will discuss graphs that have a unique hamiltonian cycle and are vertex-transitive, which means there is an automorphism that takes any vertex to any other vertex. Cycles are the only examples with finitely many vertices, but the situation is more...

In 1900, Hilbert posed the following problem: “Given a Diophantine equation with integer coefficients: to devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in (rational)...

We describe a thin family of Dirichlet L-functions which have an irregular and perhaps unexpected behavior in their value distribution. This behavior has an arithmetic explanation and corresponds to the nonvanishing of a certain Gauss type sum. We...