The Ramanujan Journal

, Volume 7, Issue 1–3, pp 343–366 | Cite as

Relations Between the Ranks and Cranks of Partitions

  • A.O.L. Atkin
  • F.G. Garvan
Article

Abstract

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.

partitions rank crank Ramanujan congruences Eisenstein series modular forms 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • A.O.L. Atkin
    • 1
  • F.G. Garvan
    • 2
  1. 1.Department of MathematicsUniversity of Illinois at ChicagoChicago
  2. 2.Department of MathematicsUniversity of FloridaGainesville

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