The asymptotic distribution of Andrews' smallest parts function
The smallest parts function \(spt(n)\) was defined by \textit{G. E. Andrews} in [J. Reine Angew. Math. 624, 133--142 (2008; Zbl 1153.11053)] and counts the number of smallest parts associated to partitions of the positive integer \(n\). This function has interesting properties and satisfies congruences similar to Ramanujan's congruences for the partition function \(p(n)\). In this paper, using methods from spectral theory of automorphic forms, the authors give an asymptotic formula with a power saving error for the function \(spt(n)\). The main application is a similar formula for the number of \(2\)-marked Durfee symbols associated to partitions of \(n\).
scientific article; zbMATH DE number 6520101
scientific article