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Asymptotic formulae for partition ranks

Volume 168 / 2015

Jehanne Dousse, Michael H. Mertens Acta Arithmetica 168 (2015), 83-100 MSC: 05A17, 11F03, 11F30, 11F50, 11P55, 11P82. DOI: 10.4064/aa168-1-5

Abstract

Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.

Authors

  • Jehanne DousseLIAFA, Université Paris Diderot
    75025 Paris Cedex 13, France
    e-mail
  • Michael H. MertensMathematisches Institut
    der Universität zu Köln
    Weyertal 86-90
    D-50931 Köln, Germany
    e-mail

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