On Rademacher's Conjecture and A Recurrence Relation of Euler

Abstract

We consider a connection between Rademacher's conjectural partial fraction decomposition for the reciprocal of Dedekind's eta function and Euler's recurrence relation for the partition function. An identity for coefficients attached to cyclotomic characteristic roots of this recurrence is obtained under a separability hypothesis. We make a divisibility conjecture for the discriminant of the characteristic polynomial which would imply separability.