Recently, Bruinier and Ono investigated the arithmetic of the coefficients of Ramanujan’s mock theta function ω(q). In Ramanujan J. (submitted) they obtained congruences with respect to the modulus 512. Here we show that ω(q) modulo 5 is dictated by an elliptic curve.
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Andrews, G.E.: Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks. Invent. Math. 169, 37–73 (2007)
Bruinier, J.H., Ono, K.: Arithmetic of Borcherds’s exponents. Math. Ann. 327, 239–303 (2003)
Bruinier, J.H., Ono, K.: Heegner divisors, L-functions, and Maass forms. Ann. Math. (accepted for publication)
Bruinier, J.H., Ono, K.: Identities and congruences for the coefficients of Ramanujan’s ω(q), submitted for the special issue of the Ramanujan Journal in celebration of G.E. Andrews’s 70th Birthday
Fine, N.J.: Basic Hypergeometric Series and Applications. Math. Surveys and Monographs, vol. 27. Am. Math. Soc., Providence (1988)
Ono, K.: The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-Series. CBMS Regional Conference Series in Mathematics, vol. 102. Am. Math. Soc., Providence (2004)
Serre, J.-P.: Propriétés galoisiennes des points d’ordre fini des courbes elliptiques. Invent. Math. 15, 259–331 (1972)
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Alfes, C. Congruences for Ramanujan’s ω(q). Ramanujan J 22, 163–169 (2010). https://doi.org/10.1007/s11139-009-9183-z