Theorems · Theorem · number theory
UpperHalfPlane.IsZeroAtImInfty.of_exp_decay
∀ {E : Type u_3} [inst : NormedAddCommGroup E] {f : UpperHalfPlane → E},
(∃ c > 0, f =O[UpperHalfPlane.atImInfty] fun τ => Real.exp (-c * τ.im)) → UpperHalfPlane.IsZeroAtImInfty f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- Real.expstatement and proof · cited by 871
- UpperHalfPlanestatement and proof · cited by 626
- Filter.Tendsto.compproof · cited by 560
- Asymptotics.IsBigOstatement and proof · cited by 506
- Filter.tendsto_idproof · cited by 180
- UpperHalfPlane.imstatement and proof · cited by 128
- neg_lt_zeroproof · cited by 36
- UpperHalfPlane.atImInftystatement and proof · cited by 35
- Filter.tendsto_comapproof · cited by 30
- UpperHalfPlane.IsZeroAtImInftystatement · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- UpperHalfPlane.IsZeroAtImInfty.petersson_isZeroAtImInfty_leftproof · cited by 1
- UpperHalfPlane.IsZeroAtImInfty.petersson_isZeroAtImInfty_rightproof · cited by 0