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RamanujanTauZ

RamanujanTauZ[t]
gives the Ramanujan tau Z-function Z(t).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Z(t)=e^(i theta( t)) L(i t+6), where theta is the Ramanujan tau theta function, and L is the Ramanujan tau L-function.
  • For certain special arguments, RamanujanTauZ 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:
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Click for copyable input
Out[1]=
Scope   (5)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
RamanujanTauZ evaluates to exact values for certain special arguments:
RamanujanTauZ threads over lists:
Applications   (2)
Plot of the absolute value of RamanujanTauZ:
Find a numerical root:
Properties & Relations   (2)
On the critical line, RamanujanTauZ is the modulus of RamanujanTauL up to a sign:
RamanujanTauZ can be expressed in terms of RamanujanTauL and RamanujanTauTheta:
Evaluate derivatives numerically:
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