On the non-existence of simple congruences for quotients of Eisenstein series
Michael Dewar (2010)
Acta Arithmetica
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Displaying similar documents to “Congruences for the coefficients of quotients of Eisenstein series”
On the non-existence of simple congruences for quotients of Eisenstein series
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Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 for p3(n) by using some theta function identities. For example, we prove that for n ≥ 0, p3 (243n + 233) ≡ p3 (729n + 638) ≡ 0 (mod 310).