Theorems · Theorem · number theory
ArithmeticFunction.LSeries_positive
∀ {a : ℕ → ℂ}, 0 ≤ a → 0 < a 1 → ∀ {x : ℝ}, LSeries.abscissaOfAbsConv a < ↑x → 0 < LSeries a ↑xIf all values of a ℂ-valued arithmetic function a 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
- 0 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.ofRealstatement · cited by 1,654
- 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
- LSeries.positiveproof · cited by 3
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