Ramanujan and Transcendence

  • M. Ram Murty
  • V. Kumar Murty


In his 1916 memoir entitled “On certain arithmetic function,” Ramanujan considered the three fundamental Eisenstein series P,Q, and R. In that paper, he derived a system of nonlinear differential equations satisfied by them. These equations played a fundamental role in the 1996 work of Nesterenko who calculated the transcendence degree of the field generated by the special values of these Eisenstein series. In this chapter, we discuss the significance of this work in transcendental number theory.


Modular Form Eisenstein Series Modular Function Riemann Zeta Function Mock Modular Form 
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© 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

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