Computation at the Heart of Mathematics: Celebrating the Work of David Boyd, Recipient of the 2005 CRM-Fields Prize

One of the great themes of modern number theory is how analysis and algebra often give us the same information by somewhat different means, for example by a formula with an algebraic inter-pretation on one side and an analytic interpretation on the other.1 There is one such formula that every mathematician has been exposed to in their education, but has only recently been seriously interpreted in this way, and that is Jensen’s theorem in complex analysis: This tells us that for a function f which is analytic on a closed disk of radius r, the average value of log jf(z)j on the boundary of the disk can be determined precisely in terms of f(0) and the zeros of f inside this disk. In the particular case of an irreducible polynomial f with leading coefficient a0, and the unit disk, this leads to the formula M(f): = ja0j