Abstract

In the literature one can find evaluation of ratios of theta function $\frac{f(-q)}{q^{\frac{n-1}{24}}f(-q^n)}$ for $n=2, 4, 5, 7, 9, 25$. The purpose of this article is to obtain evaluation of $\frac{f(-q)}{q^{\frac{6}{24}}f(-q^6)}$ for certain rational $k$ with $q=e^{-2\pi\sqrt{k}}$.

Keywords and Phrases

Theta functions, Continued fraction.

A.M.S. subject classification

11J70, 14K25.

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