Geodesic
Non-Existence of Ramanujan Congruences in Modular Forms of Level Four
Canadian journal of mathematics, Tome 63 (2011) no. 6, pp. 1284-1306

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DOI

Ramanujan famously found congruences like $p(5n\,+\,4)\,\equiv \,0$ mod 5 for the partition function. We provide a method to find all simple congruences of this type in the coefficients of the inverse of a modular form on ${{\Gamma }_{1}}(4)$ that is non-vanishing on the upper half plane. This is applied to answer open questions about the (non)-existence of congruences in the generating functions for overpartitions, crank differences, and 2-colored $F$ -partitions.
DOI : 10.4153/CJM-2011-027-x
Mots-clés : 11F33, 11P83, modular form, Ramanujan congruence, generalized Frobenius partition, overpartition, crank 
Dewar, Michael. Non-Existence of Ramanujan Congruences in Modular Forms of Level Four. Canadian journal of mathematics, Tome 63 (2011) no. 6, pp. 1284-1306. doi: 10.4153/CJM-2011-027-x
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     title = {Non-Existence of {Ramanujan} {Congruences} in {Modular} {Forms} of {Level} {Four}},
     journal = {Canadian journal of mathematics},
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     year = {2011},
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     doi = {10.4153/CJM-2011-027-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-027-x/}
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