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This article concerns an old conjecture due to E. T. Whittaker, aiming to describe the group uniformizing an arbitrary hyperelliptic Riemann surface y 2 = 2g+2 i=1 (x−a i ) as an index two subgroup of the monodromy group of an explicit second order linear differential equation with singularities at the values a i . Whittaker and collaborators in the thirties, and R. Rankin some twenty years later, were able to prove the conjecture for several families of hyperelliptic surfaces, characterized bydoi:10.1090/s0002-9947-03-03441-x fatcat:3hzymutglrdovej7ppaeh3fh2e