ON THE INFINITE PRODUCTS DERIVED FROM THETA SERIES II

Title & Authors
ON THE INFINITE PRODUCTS DERIVED FROM THETA SERIES II
Kim, Dae-Yeoul; Koo, Ja-Kyung;

Abstract
Let k be an imaginary quadratic field, $\small{{\eta}}$ the complex upper half plane, and let $\small{{\tau}{\in}{\eta}{\cap}k,\;q=e^{{\pi}{i}{\tau}}}$. For n, t $\small{{\in}{\mathbb{Z}}^+}$ with $\small{1{\leq}t{\leq}n-1}$, set n=$\small{{\delta}{\cdot}2^{\iota}}$($\small{{\delta}}$=2, 3, 5, 7, 9, 13, 15) with $\small{{\iota}{\geq}0}$ integer. Then we show that $\small{q{\frac}{n}{12}-{\frac}{t}{2}+{\frac}{t^2}{2n}{\prod}_{m=1}^{\infty}(1-q^{nm-t})(1-q^{{nm}-(n-t)})}$ are algebraic numbers.
Keywords
algebraic number;theta series;Rogers-Ramanujan identities;
Language
English
Cited by
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