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RamanujanTauTheta

RamanujanTauTheta[t]
gives the Ramanujan tau theta function theta(t).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Apart from a sign, theta(t) gives the phase of the Ramanujan L-function L(6+it).
  • For certain special arguments, RamanujanTauTheta automatically evaluates to exact values.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Evaluate numerically:
Plot on the real line:
Evaluate numerically:
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Click for copyable input
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Plot on the real line:
In[1]:=
Click for copyable input
Out[1]=
Scope   (4)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
RamanujanTauTheta threads over lists:
Applications   (2)
Contour plot of the absolute value of RamanujanTauTheta:
The first 10 Gram points of RamanujanTauL:
Plot of RamanujanTauZ and Gram points:
Properties & Relations   (1)
On the critical line, RamanujanTauTheta gives the phase of RamanujanTauL up to a sign:
RamanujanTauL can be expressed in terms of RamanujanTauTheta:
Possible Issues   (1)
Machine-number inputs can give high-precision results:
Neat Examples   (1)
Density plot of the argument:
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