Theorems · Theorem · number theory
LSeries.abscissaOfAbsConv_le_of_le_const_mul_rpow
∀ {f : ℕ → ℂ} {x : ℝ}, (∃ C, ∀ (n : ℕ), n ≠ 0 → ‖f n‖ ≤ C * ↑n ^ x) → LSeries.abscissaOfAbsConv f ≤ ↑x + 1If ‖f n‖ is bounded by a constant times n^x, then the abscissa of absolute convergence
of f is bounded by x + 1.
- Defined in
- Mathlib.NumberTheory.LSeries.Convergence
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- Norm.normstatement and proof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- LE.le.trans_ltproof · cited by 795
- ERealstatement · cited by 793
- Real.toERealstatement and proof · cited by 303
- LT.lt.falseproof · cited by 66
- LSeries.abscissaOfAbsConvstatement and proof · cited by 50
- EReal.coe_lt_coe_iffproof · cited by 15
- EReal.exists_between_coe_realproof · cited by 3
- LSeriesSummable.abscissaOfAbsConv_leproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LSeries.abscissaOfAbsConv_le_of_le_constproof · cited by 0