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Theorems · Theorem · number theory

ArithmeticFunction.LSeriesSummable_moebius_iff

∀ {s : ℂ}, LSeriesSummable (fun n => ↑(ArithmeticFunction.moebius n)) s ↔ 1 < s.re

The L-series of the Möbius function converges absolutely at s if and only if re s > 1.

Defined in
Mathlib.NumberTheory.LSeries.Dirichlet
Cited by
2 results in Mathlib
Foundations
Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

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