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- W2963758336 abstract "Let $$f(q):=1+sum _{n=1}^{infty } alpha (n)q^n$$ be the well-known third order mock theta of Ramanujan. In 1964, George Andrews proved an asymptotic formula of the form $$begin{aligned} alpha (n)= sum _{cle sqrt{n}} psi (n)+O_epsilon left( n^epsilon right) , end{aligned}$$ where $$psi (n)$$ is an expression involving generalized Kloosterman sums and the I-Bessel function. Andrews conjectured that the series converges to $$alpha (n)$$ when extended to infinity, and that it does not converge absolutely. Bringmann and Ono proved the first of these conjectures. Here we obtain a power savings bound for the error in Andrews’ formula, and we also prove the second of these conjectures. Our methods depend on the spectral theory of Maass forms of half-integral weight, and in particular on an average estimate for the Fourier coefficients of such forms which gives a power savings in the spectral parameter. As a further application of this result, we derive a formula which expresses $$alpha (n)$$ with small error as a sum of exponential terms over imaginary quadratic points (this is similar in spirit to a recent result of Masri). We also obtain a bound for the size of the error term incurred by truncating Rademacher’s analytic formula for the ordinary partition function which improves a result of the first author and Andersen when $$24n-23$$ is squarefree." @default.
- W2963758336 created "2019-07-30" @default.
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- W2963758336 date "2019-04-23" @default.
- W2963758336 modified "2023-10-17" @default.
- W2963758336 title "Maass forms and the mock theta function f(q)" @default.
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- W2963758336 doi "https://doi.org/10.1007/s00208-019-01829-0" @default.
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