The asymptotic distribution of Andrews' smallest parts function Academic Article

abstract

• 2015, Springer Basel. 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 0(N).

authors

• Masri, Mohamad

published proceedings

• ARCHIV DER MATHEMATIK

author list (cited authors)

• Banks, J., Barquero-Sanchez, A., Masri, R., & Sheng, Y.

citation count

• 3

publication date

• December 2015

publisher

• Springer Nature  Publisher

keywords

• Durfee Symbol
• Partition
• Smallest Parts Function

Digital Object Identifier (DOI)

• 10.1007/s00013-015-0831-9

start page

• 539

end page

• 555

volume

• 105

issue

• 6

URL

• http://dx.doi.org/10.1007/s00013-015-0831-9