Ramanujan’s Conjecture and -Adic Representations

  • M. Ram Murty
  • V. Kumar Murty


Ramanujan discovered some remarkable congruences satisfied by the τ-function. In retrospect, these congruences are now better understood via the theory of -adic representations. We present a short survey of these ideas and indicate the relationship between Ramanujan’s conjecture on the growth of τ(n) with the celebrated Weil conjectures, formulated by André Weil in 1949. These conjectures inspired the rapid development of modern algebraic geometry.


Zeta Function Modular Form Elliptic Curve Characteristic Polynomial Elliptic Curf 
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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

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