Amir Akbary

This is the fourth in a series of conferences, the previous three being held at the University of Seville, Seville, Spain (2007); National University of Ireland, Galway, Ireland (2009); and RMIT, Melbourne, Australia (2011). The 2014 (ADTHM) will be...

Collectively, the number theorists taken from the principal mathematics departments in Alberta -- at the universities of Alberta, Calgary and Lethbridge -- form a very strong group, with researchers being recognized not just in Canada, but globally...

We will describe the celebrated ABC conjecture, due to Oesterle and Masser, formulated in 1985. We will explain one of the motivations behind this conjecture and discuss a refinement of this conjecture put forward by Baker in 1996.

We describe heuristics for several well-known density conjectures in prime number theory and elliptic curves theory. In each case we show how one can arrive at explicit expressions for density constants. The conjectures include twin prime conjecture...

For a prime p, let n(p) be the number of solutions (x, y) of y^2 = x^3 + ax + b over the finite field F_p and let a(p) = p - n(p). In 1976, Serge Lang and Hale Trotter formulated a conjecture regarding the distribution of primes p for which a(p) = A...

We describe a theorem of M. Mourtada and V. Kumar Murty on the distribution of values of the logarithmic derivative of the L-functions attached to quadratic characters. Under the assumption of the generalized Riemann Hypothesis they prove the...

An "elliptic sequence" is a solution over an arbitrary integral domain of the recursion W(m+n) W(m-n) = W(m+1) W(m-1) W(n)^2 - W(n+1) W(n-1) W(m)^2, where m and n are integers. The theory of integral elliptic sequences was developed by Morgan Ward in...

It is known that if the negative Pell equation X2−DY2=−1 is solvable (in integers), and if (x,y) is its solution with smallest positive x and y, then all of its solutions (xn,yn) are given by the formula xn + yn√D = ±(x + y√D) 2n+1 for n∈Z...

We describe a theorem due to Jianya Liu and Yangbo Ye (Pure and Applied Mathematics Quarterly, Volume 3, Number 2, 481-497, 2007) concerning the prime number theorem for automorphic L-functions. We state the theorem and review the strategy of the...

We describe a theorem due to Jianya Liu and Yangbo Ye (Pure and Applied Mathematics Quarterly, Volume 3, Number 2, 481-497, 2007) concerning the prime number theorem for automorphic L-functions. We state the theorem and review the strategy of the...