Theorems · Theorem · number theory
LSeries.positive
∀ {a : ℕ → ℂ}, 0 ≤ a → 0 < a 1 → ∀ {x : ℝ}, LSeries.abscissaOfAbsConv a < ↑x → 0 < LSeries a ↑xIf all values of a : ℕ → ℂ are nonnegative reals and a 1 is positive,
then L a x is positive real for all real x larger than abscissaOfAbsConv a.
- Defined in
- Mathlib.NumberTheory.LSeries.Positivity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Complexstatement and proof · cited by 5,565
- Complex.ofRealstatement and proof · cited by 1,654
- one_ne_zeroproof · cited by 885
- ERealstatement · cited by 793
- Real.toERealstatement and proof · cited by 303
- LSeriesstatement · cited by 77
- Complex.partialOrderstatement · cited by 64
- LSeries.abscissaOfAbsConvstatement and proof · cited by 50
- LSeriesSummable_of_abscissaOfAbsConv_lt_reproof · cited by 9
- Summable.tsum_posproof · cited by 3
- LSeries.term_nonnegproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- riemannZeta_pos_of_one_ltproof · cited by 2
- LSeries.positive_of_differentiable_of_eqOnproof · cited by 1
- ArithmeticFunction.LSeries_positiveproof · cited by 0