Nickolas AndersenAffiliation: University of Illinois Email: nandrsn4@illinois.edu Title Of Talk: Algebraic and transcendental formulas for the smallest parts function URL: http://arxiv.org/pdf/1504.02500v2.pdf 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 BruinierOno for the ordinary partition function. The convergence of our expression is nontrivial; the proof relies on a power savings estimate for weighted sums of Kloosterman sums of halfintegral weight which follows from spectral methods. This is joint work with Scott Ahlgren. WARNING: This page contains MATHJAX
Last update made Tue Feb 9 06:33:00 PST 2016.
