Theorems · Theorem · number theory
Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log
∀ {x : ℝ}, 1 ≤ x → |Chebyshev.psi x - Chebyshev.theta x| ≤ 2 * √x * Real.log x|ψ x - θ x| ≤ c √ x log x with an explicit constant c. To remove the log, see
psi_sub_theta_le_mul_sqrt.
- Defined in
- Mathlib.NumberTheory.Chebyshev
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites58
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
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- absstatement and proof · cited by 1,814
- le_of_ltproof · cited by 1,175
- le_transproof · cited by 985
- Real.logstatement and proof · cited by 939
Cited by2
Results whose statement or proof uses this declaration.
- Chebyshev.psi_sub_theta_leproof · cited by 2
- Chebyshev.psi_leproof · cited by 1