Theorems · Theorem · number theory
LSeriesSummable.convolution
∀ {f g : ℕ → ℂ} {s : ℂ}, LSeriesSummable f s → LSeriesSummable g s → LSeriesSummable (LSeries.convolution f g) sThe L-series of the convolution product f ⍟ g of two sequences f and g
is summable when both L-series are summable.
- Defined in
- Mathlib.NumberTheory.LSeries.Convolution
- Cited by
- 2 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- LSeriesSummablestatement and proof · cited by 59
- LSeries.convolutionstatement · cited by 18
- LSeriesSummable.LSeriesHasSumproof · cited by 5
- LSeriesHasSum.convolutionproof · cited by 3
- LSeriesHasSum.LSeriesSummableproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ArithmeticFunction.LSeriesSummable_mulproof · cited by 1
- LSeries.abscissaOfAbsConv_convolution_leproof · cited by 0