Polynomial analogues of Ramanujan congruences for Han's hooklength formula
Volume 160 / 2013
Acta Arithmetica 160 (2013), 303-315
MSC: Primary 05A10; Secondary 05A17.
DOI: 10.4064/aa160-4-1
Abstract
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.
