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20 Theta FunctionsProperties20.3 Graphics

Figure 20.3.2 (See in context.)

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Figure 20.3.2: θ1(πx,q), 0x2, q = 0.05, 0.5, 0.7, 0.9. For qqDedekind, θ1(πx,q) is convex in x for 0<x<1. Here qDedekind=e-πy0=0.19 approximately, where y=y0 corresponds to the maximum value of Dedekind’s eta function η(iy) as depicted in Figure 23.16.1. Magnify