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.
De Scott Ahlgren
De Boris Pioline
De Juan Camilo Arosemena Serrato
De Victor Kleptsyn
De Joaquin Brum
De Emmanuel Militon
De Albert Schwarz
De Juan Camilo Arosemena Serrato
De Francesca Arici
De Amine Marrakchi
