Mock Theta Functions and Mock Modular Forms

  • M. Ram Murty
  • V. Kumar Murty


In 1920, three months before his untimely death, Ramanujan hastily described the beginnings of a new theory he called “mock theta functions.” In 2001, Zwegers in his doctoral thesis, discovered the relation between non-holomorphic modular forms, indefinite theta series, and “mock theta functions.” We briefly describe this development in this chapter.


Modular Form Theta Function Jacobi Form Mock Theta Function Maass Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 7.
    G.E. Andrews, An introduction to Ramanujan’s “lost” notebook. Am. Math. Mon. 86, 89–108 (1979) MATHCrossRefGoogle Scholar
  2. 26.
    J. Bruinier, K. Ono, Heegner divisors, L-functions and harmonic weak Maass forms. Ann. of Math. 172, 2135–2181 (2010) MathSciNetMATHCrossRefGoogle Scholar
  3. 45.
    F. Dyson, A walk through Ramanujan’s garden, in Ramanujan Revisited (Academic Press, Boston, 1988), pp. 7–28 Google Scholar
  4. 78.
    D.R. Hickerson, A proof of the mock theta conjectures. Invent. Math. 94, 639–660 (1988) MathSciNetMATHCrossRefGoogle Scholar
  5. 79.
    D.R. Hickerson, On the seventh order mock theta functions. Invent. Math. 94, 661–677 (1988) MathSciNetMATHCrossRefGoogle Scholar
  6. 152.
    K. Ono, Unearthing the visions of a master, in Harmonic Maass forms and Number Theory. Current Developments in Mathematics, (2008), pp. 347–454 Google Scholar
  7. 206.
    D. Zagier, Ramanujan’s mock theta functions and their applications, (d’après Zwegers and Bringmann-Ono). Sem. Bourbaki 60(986) (2007) Google Scholar

Copyright information

© Springer India 2013

Authors and Affiliations

  • M. Ram Murty
    • 1
  • V. Kumar Murty
    • 2
  1. 1.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

Personalised recommendations