Theorems · Theorem · number theory
Chebyshev.psi_eq_theta_add_sum_theta
∀ {x : ℝ},
2 ≤ x →
Chebyshev.psi x = Chebyshev.theta x + ∑ n ∈ Finset.Icc 2 ⌊Real.log x / Real.log 2⌋₊, Chebyshev.theta (x ^ (1 / ↑n))- Defined in
- Mathlib.NumberTheory.Chebyshev
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.sumstatement · cited by 5,195
- le_reflproof · cited by 2,061
- Real.logstatement and proof · cited by 939
- Finset.Iccstatement · cited by 348
- Nat.floorstatement and proof · cited by 215
- Chebyshev.thetastatement · cited by 38
- Chebyshev.psistatement · cited by 34
- Chebyshev.psi_eq_theta_add_sum_theta'proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Chebyshev.theta_le_psiproof · cited by 3
- Chebyshev.abs_psi_sub_theta_le_sqrt_mul_logproof · cited by 2