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Polynomial analogues of Ramanujan congruences for Han's hooklength formula

Volume 160 / 2013

William J. Keith 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.

Authors

  • William J. KeithMichigan Technological University
    Fisher Hall 319
    1400 Townsend Drive
    Houghton, MI 49931, U.S.A.
    e-mail

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