Theorems · Theorem · number theory
Chebyshev.psi_eq_sum_mul_log_prime
∀ (n : ℕ), Chebyshev.psi ↑n = ∑ p ∈ n.primesLE, ↑(Nat.log p n) * Real.log ↑p
- Defined in
- Mathlib.NumberTheory.Chebyshev
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- SetLike.coeproof · cited by 8,199
- Finset.sumstatement and proof · cited by 5,195
- LE.le.transproof · cited by 3,151
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- Nat.Primeproof · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- Finset.filterproof · cited by 949
Cited by2
Results whose statement or proof uses this declaration.
- Chebyshev.psi_le_primeCounting_mul_logproof · cited by 3
- Chebyshev.psi_eq_log_lcmUptoproof · cited by 1