This talk is a report on work in progress with Massimo Bertolini. I will briefly describe a classical method of Kronecker which constructs a solution to Pell's equation from special values of the Dedekind eta-function. I will then discuss how this method can be transposed to the setting of elliptic curves, to prove some special cases of a conjecture on ``Stark-Heegner points" attached to ring class fields of real quadratic fields. This leads to a new p-adic analytic construction of points on elliptic curves in terms of the modular symbols of Birch and Manin.