In the 1980s, Andrews studied certain q-hypergeometric series from Ramanujan’s ``Lost" Notebook, and made several conjectures on their Fourier coefficients, which encode partition theoretic information. The corresponding conjectures on the coefficients of Ramanujan’s $\sigma(q)$ were resolved by Andrews, Dyson and Hickerson, who related them to the arithmetic of $\mathbb Q(\sqrt{6})$. Cohen also made connections to Maass waveforms. In this work, by new methods, we prove additional conjectures of Andrews, e.g., we blend novel techniques inspired by Garoufalidis' and Zagier's recent work on asymptotics of Nahm sums with classical techniques such as the Circle Method in Analytic Number Theory.

This is joint work with Joshua Males, Larry, Rolen, and Matthias Storzer.