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Built-in
Mathematica
Symbol
Special Functions
Tutorials »
|
RiemannSiegelTheta
Zeta
ZetaZero
RamanujanTauZ
See Also »
|
Analytic Number Theory
Multiplicative Number Theory
Number Theoretic Functions
Prime Numbers
Special Functions
Zeta Functions & Polylogarithms
More About »
RiemannSiegelZ
RiemannSiegelZ
[
t
]
gives the Riemann-Siegel function
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
, where
is the Riemann-Siegel theta function, and
is the Riemann zeta function.
for real
.
is an analytic function of
except for branch cuts on the imaginary axis running from
to
.
For certain special arguments,
RiemannSiegelZ
automatically evaluates to exact values.
RiemannSiegelZ
can be evaluated to arbitrary numerical precision.
RiemannSiegelZ
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
In[1]:=
Out[1]=
Find a numerical root:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
Scope
(7)
Applications
(5)
Properties & Relations
(2)
Possible Issues
(2)
Neat Examples
(3)
SEE ALSO
RiemannSiegelTheta
Zeta
ZetaZero
RamanujanTauZ
TUTORIALS
Special Functions
RELATED LINKS
Demonstrations with RiemannSiegelZ
(
Wolfram Demonstrations Project
)
MathWorld
The Wolfram Functions Site
NKS|Online
(
A New Kind of Science
)
MORE ABOUT
Analytic Number Theory
Multiplicative Number Theory
Number Theoretic Functions
Prime Numbers
Special Functions
Zeta Functions & Polylogarithms
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