Skip to main content

Congruences for Ramanujan’s ω(q)


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.

This is a preview of subscription content, access via your institution.


  1. Andrews, G.E.: Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks. Invent. Math. 169, 37–73 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bruinier, J.H., Ono, K.: Arithmetic of Borcherds’s exponents. Math. Ann. 327, 239–303 (2003)

    Article  MathSciNet  Google Scholar 

  3. Bruinier, J.H., Ono, K.: Heegner divisors, L-functions, and Maass forms. Ann. Math. (accepted for publication)

  4. 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

  5. Fine, N.J.: Basic Hypergeometric Series and Applications. Math. Surveys and Monographs, vol. 27. Am. Math. Soc., Providence (1988)

    MATH  Google Scholar 

  6. 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)

    Google Scholar 

  7. Serre, J.-P.: Propriétés galoisiennes des points d’ordre fini des courbes elliptiques. Invent. Math. 15, 259–331 (1972)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Claudia Alfes.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Alfes, C. Congruences for Ramanujan’s ω(q). Ramanujan J 22, 163–169 (2010).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Mathematics Subject Classification (2000)