Geodesic
On the transcendence of moduli of the Jacobian elliptic functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 167-172.

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Let $\mathrm{sn}_1z$ and $\mathrm{sn}_2z$ be the Jacobian elliptic functions of moduli $\varkappa_1$ and $\varkappa_2$, $0\varkappa_1^21$, $0\varkappa_2^21$, $\tau_1$ and $\tau_2$ be the values of the modular variable, $\theta_3(\tau_1)$ and $\theta_3(\tau_2)$ be the theta constants. In this paper, the set $\varkappa_1$, $\varkappa_2$, $\theta_3(\tau_1)$, and $\theta_3(\tau_2)$ is shown to contain a transcendental number, provided that $\tau_1/\tau_2$ is irrational. 
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Ya. M. Kholyavka. On the transcendence of moduli of the Jacobian elliptic functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 167-172. http://geodesic.mathdoc.fr/item/FPM_2010_16_6_a12/

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