Algebraic integers as special values of modular units
Algebraic integers as special values of modular units
Abstract Let $\varphi(\tau)=\eta(\tfrac12(\tau+1))^2/\sqrt{2\pi}\exp\{\tfrac14\pi\ri\}\eta(\tau+1)$ , where η(τ) is the Dedekind eta function. We show that if τ 0 is an imaginary quadratic argument and m is an odd integer, then $\sqrt{m}\varphi(m\tau_0)/\varphi(\tau_0)$ is an algebraic integer dividing $\sqrt{m}$ This is a generalization of a result of Berndt, Chan and Zhang. On the …