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Polynomial analogues of Ramanujan congruences for Han's hooklength formula

William J. Keith — 2013

Acta Arithmetica

This article considers the eta power $\prod_{(1 - q^{k})}^{b - 1}$ . It is proved that the coefficients of $q^{n} / n!$ in this expression, as polynomials in b, exhibit equidistribution of the coefficients in the nonzero residue classes mod 5 when n = 5j+4. Other symmetries, as well as symmetries for other primes and prime powers, are proved, and some open questions are raised.

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