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1: 21.3 Symmetry and Quasi-Periodicity
§21.3 Symmetry and Quasi-Periodicity
21.3.3 θ ( z + m 1 + Ω m 2 | Ω ) = e - 2 π i ( 1 2 m 2 Ω m 2 + m 2 z ) θ ( z | Ω ) ,
This is the quasi-periodicity property of the Riemann theta function. …
2: 20.2 Definitions and Periodic Properties
§20.2(ii) Periodicity and Quasi-Periodicity
The theta functions are quasi-periodic on the lattice: …
3: 22.16 Related Functions
Quasi-Periodicity
Quasi-Addition and Quasi-Periodic Formulas
4: 21.9 Integrable Equations
The KP equation has a class of quasi-periodic solutions described by Riemann theta functions, given by …
5: 23.2 Definitions and Periodic Properties
The function ζ ( z ) is quasi-periodic: for j = 1 , 2 , 3 , … For further quasi-periodic properties of the σ -function see Lawden (1989, §6.2).
6: 21.4 Graphics
See accompanying text
Figure 21.4.4: A real-valued scaled Riemann theta function: θ ^ ( i x , i y | Ω 1 ) , 0 x 4 , 0 y 4 . In this case, the quasi-periods are commensurable, resulting in a doubly-periodic configuration. Magnify 3D Help