Theorems · Theorem · number theory
LSeries_one_eq_riemannZeta
∀ {s : ℂ}, 1 < s.re → LSeries 1 s = riemannZeta sThe L-series of the constant sequence 1 equals the Riemann Zeta Function on its
domain of convergence 1 < re s.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 306 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 · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.restatement and proof · cited by 882
- riemannZetastatement · cited by 85
- LSeriesstatement · cited by 77
- ArithmeticFunction.LSeries_zeta_eqproof · cited by 3
- ArithmeticFunction.LSeries_zeta_eq_riemannZetaproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- riemannZeta_pos_of_one_ltproof · cited by 2
- riemannZeta_ne_zero_of_one_lt_reproof · cited by 1
- riemannZeta_eq_exp_LSeriesproof · cited by 1
- LSeriesHasSum_oneproof · cited by 0
- riemannZeta_eulerProduct_exp_logproof · cited by 0
- ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_divproof · cited by 0