Theorems · Theorem · number theory
HurwitzZeta.isBigO_atTop_sinKernel
∀ (a : UnitAddCircle), ∃ p, 0 < p ∧ HurwitzZeta.sinKernel a =O[Filter.atTop] fun x => Real.exp (-p * x)
The function sinKernel a has exponential decay at +∞, for any a.
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- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites45
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
- Norm.normproof · cited by 5,413
- add_zeroproof · cited by 2,707
- Filter.atTopstatement and proof · cited by 2,405
- LT.lt.leproof · cited by 2,189
- SummationFilter.unconditionalproof · cited by 2,068
- le_reflproof · cited by 2,061
- Real.piproof · cited by 1,774
- Filter.univ_mem'proof · cited by 1,672
- mul_assocproof · cited by 1,667
- Filter.mp_memproof · cited by 1,537
- tsumproof · cited by 1,148
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