FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 6, PAGES 167-172

On the transcendence of moduli of the Jacobian elliptic functions

Ya. M. Kholyavka

Abstract

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Let $sn$₁ z and $sn$₂ z be the Jacobian elliptic functions of moduli $\kappa$₁ and $\kappa$₂, ₁² < 1, ₂² < 1, $$t₁ and $$t₂ be the values of the modular variable, $$q₃(t₁) and $$q₃(t₂) be the theta constants. In this paper, the set $\kappa$₁, $\kappa$₂, $$q₃(t₁), and $$q₃(t₂) is shown to contain a transcendental number, provided that $$t₁/t₂ is irrational.

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Last modified: July 5, 2011