Polynomial analogues of Ramanujan congruences for
Han's hooklength formula
Acta Arithmetica, Tome 160 (2013) no. 4, pp. 303-315
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
article considers eta power prod q b proved coefficients expression polynomials exhibit equidistribution coefficients nonzero residue classes mod other symmetries symmetries other primes prime powers proved questions raised
Affiliations des auteurs :
William J. Keith 1
William J. Keith. Polynomial analogues of Ramanujan congruences for Han's hooklength formula. Acta Arithmetica, Tome 160 (2013) no. 4, pp. 303-315. doi: 10.4064/aa160-4-1
@article{10_4064_aa160_4_1,
author = {William J. Keith},
title = {Polynomial analogues of {Ramanujan} congruences for
{Han's} hooklength formula},
journal = {Acta Arithmetica},
pages = {303--315},
year = {2013},
volume = {160},
number = {4},
doi = {10.4064/aa160-4-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa160-4-1/}
}
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