DLMF: Figure 21.4.4 ‣ §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 21.4.4 (See in context.)

Figure 21.4.4: A real-valued scaled Riemann theta function:

\hat{\theta}\left(ix,iy\middle|\boldsymbol{{\Omega}}_{1}\right)

,

0\leq x\leq 4

,

0\leq y\leq 4

. In this case, the quasi-periods are commensurable, resulting in a doubly-periodic configuration.

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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 and $\boldsymbol{{\Omega}}$ : a Riemann matrix
Permalink:: http://dlmf.nist.gov/21.4.F4.viz

21.4 Graphics 21.5 Modular Transformations

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