Bounds for Coefficients of the $f(q)$ Mock Theta Function and Applications to Partition Ranks

Abstract

We compute effective bounds for $\hat{I}\pm (n)$, the Fourier coefficients of Ramunujan's mock theta function $f(q)$ utilizing a finite algebraic formula due to Bruinier and Schwagenscheidt. We then use these bounds to prove two conjectures of Hou and Jagadeesan on the convexity and maximal multiplicative properties of the even and odd partition rank counting functions.

19 + epsilon pages