On Dwork's accessory parameter problem

We study the question which ordinary second order linear differential equation allows power series solutions whose p-adic radius of convergence is at least one, a question raised by B.Dwork. In particular we shall consider the case of Fuchsian equations with four singularities and local exponent differences 0. Received: 28 August 2000; final form: 20 November 2001/ Published online: 17 June 2002 RID="*" ID="*" Part of this work was supported by EPSRC grant L99920