Nickolas Andersen

Affiliation: University of Illinois


Title Of Talk: Algebraic and transcendental formulas for the smallest parts function


Abstract: We study the smallest parts function $\spt(n)$ introduced by Andrews. The generating function for $\spt(n)$ forms a component of a natural mock modular form of weight $3/2$ whose shadow is the Dedekind eta function. We obtain two formulas for $\spt(n)$ which are analogues of the formulas of Rademacher and Bruinier-Ono for the ordinary partition function. The convergence of our expression is non-trivial; the proof relies on a power savings estimate for weighted sums of Kloosterman sums of half-integral weight which follows from spectral methods. This is joint work with Scott Ahlgren.

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