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Explicit Values for Ramanujan's Theta Function ϕ(q)

2022
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Hardy-Ramanujan Journal
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This paper provides a survey of particular values of Ramanujan's theta function $\varphi(q)=\sum_{n=-\infty}^{\infty}q^{n^2}$, when $q=e^{-\pi\sqrt{n}}$, where $n$ is a positive rational number. First, descriptions of the tools used to evaluate theta functions are given. Second, classical values are briefly discussed. Third, certain values due to Ramanujan and later authors are given. Fourth, the methods that are used to determine these values are described. Lastly, an incomplete evaluation

doi:10.46298/hrj.2022.8923
fatcat:iyi3ctpddffwro4dv2vr7icjzq