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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.
Mathematics Subject
Classification (2000):
Primary 11P82, 11R09; Secondary 11C20, 11T40
Quaestiones Mathematicae 25 (2002), 317-325
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.
Mathematics Subject
Classification (2000):
Primary 11P82, 11R09; Secondary 11C20, 11T40
Quaestiones Mathematicae 25 (2002), 317-325
