# Maass forms and the mock theta function f(q)

@article{Ahlgren2019MaassFA,
title={Maass forms and the mock theta function f(q)},
author={Scott Ahlgren and Alexander Dunn},
journal={Mathematische Annalen},
year={2019},
pages={1-38}
}
• Published 4 June 2018
• Mathematics
• Mathematische Annalen
Let $$f(q):=1+\sum _{n=1}^{\infty } \alpha (n)q^n$$f(q):=1+∑n=1∞α(n)qn be the well-known third order mock theta of Ramanujan. In 1964, George Andrews proved an asymptotic formula of the form \begin{aligned} \alpha (n)= \sum _{c\le \sqrt{n}} \psi (n)+O_\epsilon \left( n^\epsilon \right) , \end{aligned}α(n)=∑c≤nψ(n)+Oϵnϵ,where $$\psi (n)$$ψ(n) is an expression involving generalized Kloosterman sums and the I-Bessel function. Andrews conjectured that the series converges to $$\alpha (n)$$α(n…
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