On the transcendence of moduli of the jacobian elliptic functions |
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| Authors: | Ya M Kholyavka |
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| Institution: | 1.Ivan Franko National University of L’viv,L’viv,Ukraine |
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| Abstract: | Let sn1
z and sn2
z be the Jacobian elliptic functions of moduli κ
1 and κ
2, 0 <
k12 \kappa_1^2
< 1, 0 <
k22 \kappa_2^2
< 1, τ
1 and τ
2 be the values of the modular variable, and θ
3(τ
1) and θ
3(τ
2) be the theta constants. In this paper, the set κ
1, κ
2, θ
3(τ
1), and θ
3(τ
2) is shown to contain a transcendental number, provided that τ
1
/τ
2 is irrational. |
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| Keywords: | |
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