Theorems · Theorem · number theory
ArithmeticFunction.LSeries_vonMangoldt_eq
∀ {s : ℂ}, 1 < s.re → LSeries (fun n => ↑(ArithmeticFunction.vonMangoldt n)) s = -deriv (LSeries 1) s / LSeries 1 sThe L-series of the von Mangoldt function Λ equals the negative logarithmic derivative
of the L-series of the constant sequence 1 on its domain of convergence re s > 1.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- ArithmeticFunction.vonMangoldtstatement and proof · cited by 40
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_divproof · cited by 0