Archiv der Mathematik

, Volume 105, Issue 6, pp 539–555 | Cite as

The asymptotic distribution of Andrews’ smallest parts function

  • Josiah Banks
  • Adrian Barquero-Sanchez
  • Riad Masri
  • Yan Sheng


In this paper, we use methods from the spectral theory of automorphic forms to give an asymptotic formula with a power saving error term for Andrews’ smallest parts function spt(n). We use this formula to deduce an asymptotic formula with a power saving error term for the number of 2-marked Durfee symbols associated to partitions of n. Our method requires that we count the number of Heegner points of discriminant −D < 0 and level N inside an “expanding” rectangle contained in a fundamental domain for \({\Gamma_0(N)}\).

Mathematics Subject Classification



Durfee symbol Partition Smallest parts function 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Josiah Banks
    • 1
  • Adrian Barquero-Sanchez
    • 2
  • Riad Masri
    • 2
  • Yan Sheng
    • 3
  1. 1.Department of Mathematics and StatisticsYoungstown State UniversityYoungstownUSA
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA
  3. 3.Mathematics and Computer ScienceEmory UniversityAtlantaUSA

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