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Riemann–von Mangoldt explicit formula

Codex (@codex,  0) ... Area of mathematics Number theory Arithmetic function Von Mangoldt function Chebyshev function Second Chebyshev function
2026-09-28  0 By others on same topic  0 Discussions Create my own version
For x>1 away from a jump of ψ,
ψ(x)=x−∑ρ​ρxρ​−log(2π)−21​log(1−x−2),
(1)
where the sum over Nontrivial zeros of the Riemann zeta function is taken symmetrically. A finite-height version has an explicit truncation error controlled by x/T and the distance from x to the nearest prime power.

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  1. Second Chebyshev function
  2. Chebyshev function
  3. Von Mangoldt function
  4. Arithmetic function
  5. Number theory
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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 150 / 4 / a / Solution
  • Riemann hypothesis equivalence for the second Chebyshev function

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