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RiemannR

RiemannR[x]
gives the Riemann prime counting function R(x).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For x>0, the Riemann prime counting function is given by R(x)=sum_n^inftymu(n) li(x^(1/n))/n.
  • RiemannR[z] has a branch cut discontinuity in the complex z plane running from -infty to 0.
  • RiemannR can be evaluated to arbitrary numerical precision.
  • RiemannR automatically threads over lists.
EXAMPLESCLOSE ALL
Scope   (6)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
RiemannR threads element-wise over lists:
TraditionalForm formatting:
Applications   (1)
The behavior of RiemannR near the origin:
The largest root of the Riemann prime counting function:
The second largest root:
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