Theorems · Definition · number theory
Chebyshev.theta
ℝ → ℝ
The sum of log p over primes p ≤ x.
- Defined in
- Mathlib.NumberTheory.Chebyshev
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Nat.Primeproof · cited by 2,059
- Finset.filterproof · cited by 949
- Real.logproof · cited by 939
- Finset.Iocproof · cited by 301
- Nat.floorproof · cited by 215
Cited by38
Results whose statement or proof uses this declaration.
- Chebyshev.theta_eq_zero_of_lt_twostatement · cited by 6
- Chebyshev.theta_le_log4_mul_xstatement · cited by 4
- Chebyshev.theta_eq_sum_Iccstatement · cited by 3
- Chebyshev.theta_le_psistatement and proof · cited by 3
- Chebyshev.theta_nonnegstatement · cited by 3
- Chebyshev.abs_psi_sub_theta_le_sqrt_mul_logstatement and proof · cited by 2
- Chebyshev.integral_theta_div_log_sq_isBigOstatement and proof · cited by 2
- Chebyshev.primeCounting_eq_theta_div_log_add_integralstatement and proof · cited by 2
- Chebyshev.psi_eq_sum_theta'statement and proof · cited by 2
- Chebyshev.psi_eq_theta_add_sum_thetastatement · cited by 2
- Chebyshev.psi_sub_theta_lestatement and proof · cited by 2
- Chebyshev.integrableOn_theta_div_id_mul_log_sqstatement and proof · cited by 1