Polynomial analogues of Ramanujan congruences for Han's hooklength formula
William J. Keith
Acta Arithmetica, Tome 161 (2013), p. 303-315 / Harvested from The Polish Digital Mathematics Library
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This article considers the eta power ∏(1-qk)b-1. It is proved that the coefficients of qn/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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:279088 
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     author = {William J. Keith},
     title = {Polynomial analogues of Ramanujan congruences for Han's hooklength formula},
     journal = {Acta Arithmetica},
     volume = {161},
     year = {2013},
     pages = {303-315},
     zbl = {1288.05006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-4-1}
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William J. Keith. Polynomial analogues of Ramanujan congruences for Han's hooklength formula. Acta Arithmetica, Tome 161 (2013) pp. 303-315. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-4-1/