[Merged by Bors] - feat(NumberTheory/LSeries/PrimesInAP): more properties of von Mangoldt on residue classes#19418
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…t on residue classes
PR summary be69ada5d4Import changes for modified filesNo significant changes to the import graph Import changes for all files
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jcommelin
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Nov 23, 2024
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There are some private defs/lemmas. But I think it makes sense, to keep them as is.
bors r+
| positivity | ||
| conv => enter [1, pk]; rw [Real.rpow_add <| hp₀ pk.1, Real.rpow_natCast] | ||
| refine (summable_prod_of_nonneg (fun _ ↦ by positivity)).mpr ⟨(fun p ↦ ?_), ?_⟩ | ||
| · dsimp only -- otherwise the `exact` below times out |
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This sounds a bit scary. But otherwise LGTM.
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…t on residue classes (#19418) This continues the sequence of PRs on the way to **Dirichlet's Theorem**. This one adds some properties of the von Mangoldt function `Λ` restricted to a residue class: if further restricted to primes, its support is the set of primes in that residue class, and the function `n ↦ Λ n / n`, restriced to non-primes in a residue class, is summable (the latter will be important in deducing information on the former). See [here](https://leanprover.zulipchat.com/#narrow/channel/144837-PR-reviews/topic/Prerequisites.20for.20PNT.20and.20Dirichlet's.20Thm/near/483904451) on Zulip.
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This continues the sequence of PRs on the way to Dirichlet's Theorem.
This one adds some properties of the von Mangoldt function
Λrestricted to a residue class: if further restricted to primes, its support is the set of primes in that residue class, and the functionn ↦ Λ n / n, restriced to non-primes in a residue class, is summable (the latter will be important in deducing information on the former).See here on Zulip.