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On arithmetic properties of values of theta-constants

Abstract

This article describes results about the transcendence and algebraic independence of values of theta constants (Nullthetawerte) and direct methods for proving these results. Values of other functions related to theta constants are discussed. We also present some conjectures and open questions.

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Correspondence to Yu. V. Nesterenko.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 95–122, 2005.

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Nesterenko, Y.V. On arithmetic properties of values of theta-constants. J Math Sci 146, 5697–5716 (2007). https://doi.org/10.1007/s10958-007-0386-9

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Keywords

  • Elliptic Function
  • Theta Function
  • Homogeneous Polynomial
  • Algebraic Number
  • Modular Function