Theorems · Theorem · number theory
Chebyshev.integral_theta_div_log_sq_isBigO
(fun x => ∫ (t : ℝ) in 2..x, Chebyshev.theta t / (t * Real.log t ^ 2)) =O[Filter.atTop] fun x => x / Real.log x ^ 2
Bound on the integral in Chebyshev.primeCounting_eq_theta_div_log_add_integral.
- Defined in
- Mathlib.NumberTheory.Chebyshev
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites53
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Filter.atTopstatement · cited by 2,405
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- absproof · cited by 1,814
- Set.Iccproof · cited by 1,702
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
Cited by2
Results whose statement or proof uses this declaration.
- Chebyshev.integral_theta_div_log_sq_isLittleOproof · cited by 1
- Chebyshev.primeCounting_sub_theta_div_log_isBigOproof · cited by 0