Number Theory Seminar

Speaker: Harthyno Rasolondraibe

Title: The Boyd-Lawton theorem for bivariate polynomials

Abstract: The (logarithmic) Mahler measure of a multivariate polynomial P is defined as the arithmetic mean of log|P| over the unit torus. In the univariate case, Jensen's formula allows one to express it as a function of the roots of P. Lehmer's conjecture asks whether there is a positive lower bound for the Mahler measure of integral univariate polynomials that are not cyclotomic. In this talk, I will:
- discuss a potential solution to this conjecture by characterizing the limit points of a particular subset of the positive real line;
- provide examples of such limit points for the bivariate case.