# §21.4 Graphics

Figure 21.4.1 provides surfaces of the scaled Riemann theta function , with

21.4.1

This Riemann matrix originates from the Riemann surface represented by the algebraic curve ; compare §21.7(i).

 (a) (b) (c) (a) (b) (c) (a) (b) (c)
Figure 21.4.1: parametrized by (21.4.1). The surface plots are of , , (suffix 1); , , (suffix 2); , , (suffix 3). Shown are the real part (a), the imaginary part (b), and the modulus (c).

For the scaled Riemann theta functions depicted in Figures 21.4.221.4.5

21.4.2

and

21.4.3
 Figure 21.4.2: , , . (The imaginary part looks very similar.) Symbols: : scaled Riemann theta function, : real part and : a Riemann matrix Referenced by: §21.4 Permalink: http://dlmf.nist.gov/21.4.F2 Encodings: VRML, X3D, pdf, png Figure 21.4.3: , , . Symbols: : scaled Riemann theta function and : a Riemann matrix Permalink: http://dlmf.nist.gov/21.4.F3 Encodings: VRML, X3D, pdf, png
 Figure 21.4.4: A real-valued scaled Riemann theta function: , , . In this case, the quasi-periods are commensurable, resulting in a doubly-periodic configuration. Symbols: : scaled Riemann theta function and : a Riemann matrix Permalink: http://dlmf.nist.gov/21.4.F4 Encodings: VRML, X3D, pdf, png Figure 21.4.5: The real part of a genus 3 scaled Riemann theta function: , , . This Riemann matrix originates from the genus 3 Riemann surface represented by the algebraic curve ; compare §21.7(i). Symbols: : scaled Riemann theta function, : real part and : a Riemann matrix Referenced by: §21.4 Permalink: http://dlmf.nist.gov/21.4.F5 Encodings: VRML, X3D, pdf, png
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