Colloquium Mathematics - Prof. Marc Hindry, Paris VII

Title: When zeta functions come to rescue elliptic curves

Abstract: I will start with the classical Mordell-Weil theorem: the group of rational points on a cubic curve (an elliptic curve) is finitely generated and discuss the question of finding bounds for the size of these generators. The formulation of this open problem makes no reference to zeta functions, but I will explain an analogy with another classical arithmetic theorem - the Brauer-Siegel theorem - which suggests that a detour via zeta functions could be very fruitful.