Theorems · Theorem · number theory
zeta_nat_eq_tsum_of_gt_one
∀ {k : ℕ}, 1 < k → riemannZeta ↑k = ∑' (n : ℕ), 1 / ↑n ^ kSpecial case of zeta_eq_tsum_one_div_nat_cpow when the argument is in ℕ, so the power
function can be expressed using naïve pow rather than cpow.
- Defined in
- Mathlib.NumberTheory.LSeries.RiemannZeta
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Nat.cast_oneproof · cited by 2,501
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- Complex.reproof · cited by 882
- riemannZetastatement · cited by 85
- Nat.cast_ltproof · cited by 80
- Complex.ofReal_reproof · cited by 34
- Complex.ofReal_natCastproof · cited by 21
- Complex.cpow_natCastproof · cited by 12
- zeta_eq_tsum_one_div_nat_cpowproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- riemannZeta_twoproof · cited by 2
- riemannZeta_two_mul_natproof · cited by 1
- tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeriesproof · cited by 1
- riemannZeta_fourproof · cited by 0