Theorems · Theorem · number theory
LSeries.tendsto_atTop
∀ {f : ℕ → ℂ}, LSeries.abscissaOfAbsConv f < ⊤ → Filter.Tendsto (fun x => LSeries f ↑x) Filter.atTop (nhds (f 1))If the L-series of f converges at some point, then f 1 is the limit of LSeries f x
as x → ∞.
- Defined in
- Mathlib.NumberTheory.LSeries.Injectivity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Top.topstatement and proof · cited by 9,680
- Filterproof · cited by 8,121
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- one_mulproof · cited by 2,841
- Filter.atTopstatement and proof · cited by 2,405
- zero_addproof · cited by 2,366
- Complex.ofRealstatement and proof · cited by 1,654
- ERealstatement · cited by 793
- CharP.cast_eq_zeroproof · cited by 357
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