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On a measure of algebraic independence of values of Jacobi elliptic functions

Abstract

In this paper, an estimate for the measure of algebraic independence is proved for values of the Jacobi elliptic function sn(z) at different algebraic points.

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Correspondence to Ya. M. Kholyavka.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 209–219, 2005.

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Kholyavka, Y.M. On a measure of algebraic independence of values of Jacobi elliptic functions. J Math Sci 146, 5782–5790 (2007). https://doi.org/10.1007/s10958-007-0392-y

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Keywords

  • Elliptic Function
  • Homogeneous Polynomial
  • Algebraic Number
  • Algebraic Integer
  • Homogeneous Ideal