Algebraic independence results for values of Theta-constants, II

2016/03/15 by Carsten Elsner, Elsner, Carsten, Yohei Tachiya +1 · 1 citation
Mathematics · #Meromorphic and Entire Functions #Functional Equations Stability Results #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1603.04528

Abstract

Let θ₃(τ)=1+2∑_ν=1^∞ q^ν2 with q=e^iπτ denote the Thetanullwert of the Jacobi theta function θ(z|τ) = ∑_ν=-∞^∞ e^{πiν2τ+ 2πiνz} . Moreover, let θ₂(τ)=2∑_ν=0^∞ q^(ν+1/2)² and θ₄(τ)=1+2∑_ν=1^∞ (-1)^νq^ν2. For algebraic numbers q with 0

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• Algebraic independence results for values of Jacobi theta-constants

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