DLMF: Figure 21.4.5 ‣ §21.4 Graphics ‣ Properties ‣ Chapter 21 Multidimensional Theta Functions

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21 Multidimensional Theta Functions Properties 21.4 Graphics 21.4 Graphics 21.5 Modular Transformations

Figure 21.4.5 (See in context.)

Figure 21.4.5: The real part of a genus 3 scaled Riemann theta function:

\Re\hat{\theta}\left(x+iy,0,0\middle|\boldsymbol{{\Omega}}_{2}\right)

,

0\leq x\leq 1

,

0\leq y\leq 3

. This Riemann matrix originates from the genus 3 Riemann surface represented by the algebraic curve

\mu^{3}+2\mu-\lambda^{4}=0

; compare §21.7(i).

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Annotations:

Symbols:: $\hat{\theta}\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)$ : scaled Riemann theta function, $\mathrm{i}$ : imaginary unit, $\Re$ : real part and $\boldsymbol{{\Omega}}$ : a Riemann matrix
Permalink:: http://dlmf.nist.gov/21.4.F5.viz

21.4 Graphics 21.5 Modular Transformations

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