Polynomial analogues of Ramanujan congruences for Han's hooklength formula

William J. Keith. "Polynomial analogues of Ramanujan congruences for Han's hooklength formula." Acta Arithmetica 160.4 (2013): 303-315. <http://eudml.org/doc/279088>.

@article{WilliamJ2013,
abstract = {This article considers the eta power $∏_\{(1-q^k)\}^\{b-1\}$. 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.},
author = {William J. Keith},
journal = {Acta Arithmetica},
keywords = {hooklength formula; eta power; partition function; congruences; equidistribution},
language = {eng},
number = {4},
pages = {303-315},
title = {Polynomial analogues of Ramanujan congruences for Han's hooklength formula},
url = {http://eudml.org/doc/279088},
volume = {160},
year = {2013},
}

TY - JOUR
AU - William J. Keith
TI - Polynomial analogues of Ramanujan congruences for Han's hooklength formula
JO - Acta Arithmetica
PY - 2013
VL - 160
IS - 4
SP - 303
EP - 315
AB - This article considers the eta power $∏_{(1-q^k)}^{b-1}$. 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.
LA - eng
KW - hooklength formula; eta power; partition function; congruences; equidistribution
UR - http://eudml.org/doc/279088
ER -