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RamanujanTauL

RamanujanTauL[s]
gives the Ramanujan tau Dirichlet L-function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For Re(s)>6, is given by the Dirichlet series .
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
RamanujanTauL threads over lists:
Plot on the critical line:
Find a zero of RamanujanTauL:
The number of zeros on the critical strip from 0 to :
Plot of the real part:
Ramanujan function:
Functional equation:
Approximation of RamanujanTauL using Euler product formula:
On the critical line, RamanujanTauL splits:
Evaluate derivatives numerically:
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