Theorems · Theorem · number theory
ArithmeticFunction.vonMangoldt.residueClass_eq
∀ {q : ℕ} {a : ZMod q} [NeZero q],
IsUnit a →
(fun n => ↑(ArithmeticFunction.vonMangoldt.residueClass a n)) =
(↑q.totient)⁻¹ • ∑ χ, χ a⁻¹ • fun n => χ ↑n * ↑(ArithmeticFunction.vonMangoldt n)We can express ArithmeticFunction.vonMangoldt.residueClass as a linear combination
of twists of the von Mangoldt function by Dirichlet characters.
- Defined in
- Mathlib.NumberTheory.LSeries.PrimesInAP
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
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Cites16
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- ArithmeticFunctionstatement · cited by 290
- Finset.sum_applyproof · cited by 234
- DirichletCharacterstatement and proof · cited by 161
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