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On the Parity of the Number of Partitions in Square Free Parts

  • Alexandru Zaharescu
Part of the Developments in Mathematics book series (DEVM, volume 10)

Abstract

Let \( \tilde p(n) \) be the number of partitions of a positive integer n in square free parts. We prove that for large N,
  1. (a)

    The number of nN such that \( \tilde p(n) \) is odd is ≫ log N

     
  2. (b)

    The number of nN such that \( \tilde p(n) \) is even is ≫ N/log N.

     

Key words

partition function parity problem square free numbers 

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Alexandru Zaharescu
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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