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21
Multidimensional Theta Functions
Properties
21.4
Graphics
21.4
Graphics
21.5
Modular Transformations
Figure 21.4.1
(See
in context
.)
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(a
1
)
(b
1
)
(c
1
)
(a
2
)
(b
2
)
(c
2
)
(a
3
)
(b
3
)
(c
3
)
Figure 21.4.1:
θ
^
(
𝐳
|
𝛀
)
parametrized by (
21.4.1
). The surface plots are of
θ
^
(
x
+
i
y
,
0
|
𝛀
)
,
0
≤
x
≤
1
,
0
≤
y
≤
5
(suffix 1);
θ
^
(
x
,
y
|
𝛀
)
,
0
≤
x
≤
1
,
0
≤
y
≤
1
(suffix 2);
θ
^
(
i
x
,
i
y
|
𝛀
)
,
0
≤
x
≤
5
,
0
≤
y
≤
5
(suffix 3). Shown are the real part (a), the imaginary part (b), and the modulus (c).
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ⓘ
Annotations:
Symbols:
θ
^
(
𝐳
|
𝛀
)
: scaled Riemann theta function
,
i
: imaginary unit
and
𝛀
: a Riemann matrix
Permalink:
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,
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,
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See also:
Annotations for
§21.4
and
Ch.21
