RiemannSiegelZ

RiemannSiegelZ[t]

gives the RiemannSiegel function .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • , where is the RiemannSiegel 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

open allclose all

Basic Examples  (2)

In[1]:=
Click for copyable input
Out[1]=

Find a numerical root:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Scope  (7)

Applications  (5)

Properties & Relations  (2)

Possible Issues  (2)

Neat Examples  (3)

See Also

RiemannSiegelTheta  Zeta  ZetaZero  RamanujanTauZ

Tutorials

Introduced in 1991
(2.0)