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On arithmetic properties of values of theta-constants. (English. Russian original) Zbl 1204.11124

J. Math. Sci., New York 146, No. 2, 5697-5716 (2007); translation from Fundam. Prikl. Mat. 11, No. 6, 95-122 (2005).
Summary: This article describes results about the transcendence and algebraic independence of values of theta constants (thetanullwerte) 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.

MSC:

11J89 Transcendence theory of elliptic and abelian functions
11J91 Transcendence theory of other special functions
33E05 Elliptic functions and integrals
11F27 Theta series; Weil representation; theta correspondences
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