Algebraic and transcendental formulas for the smallest parts function
Appears in collection : Automorphic forms: advances and applications / Formes automorphes: avancées et applications
We study the smallest parts function introduced by Andrews. The associated generating function forms a component of a natural mock modular form of weight 3/2 whose shadow is the Dedekind eta function. We obtain an exact formula and an algebraic formula for each value of the smallest parts function; these 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 power savings estimates for weighted sums of generalized Kloosterman sums which follow from spectral methods.
