Theorems · Theorem · number theory
LSeriesSummable_of_le_const_mul_rpow
∀ {f : ℕ → ℂ} {x : ℝ} {s : ℂ}, x < s.re → (∃ C, ∀ (n : ℕ), n ≠ 0 → ‖f n‖ ≤ C * ↑n ^ (x - 1)) → LSeriesSummable f sIf f n is bounded in absolute value by a constant times n^(x-1) and re s > x,
then the LSeries of f is summable at s.
- Defined in
- Mathlib.NumberTheory.LSeries.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites46
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
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- LE.le.transproof · cited by 3,151
- Filter.Eventuallyproof · cited by 3,134
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- Filter.atTopproof · cited by 2,405
- SummationFilter.unconditionalproof · cited by 2,068
- Nat.cast_zeroproof · cited by 1,870
- mul_assocproof · cited by 1,667
Cited by3
Results whose statement or proof uses this declaration.
- LSeriesSummable_of_bounded_of_one_lt_reproof · cited by 5
- LSeries.abscissaOfAbsConv_le_of_le_const_mul_rpowproof · cited by 1
- LSeriesSummable_of_isBigO_rpowproof · cited by 1