Abstract
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 \({\Gamma_0(N)}\).
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Banks, J., Barquero-Sanchez, A., Masri, R. et al. The asymptotic distribution of Andrews’ smallest parts function. Arch. Math. 105, 539–555 (2015). https://doi.org/10.1007/s00013-015-0831-9
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DOI: https://doi.org/10.1007/s00013-015-0831-9