Theorems · Theorem · number theory
ZMod.differentiable_completedLFunction
∀ {N : ℕ} [inst : NeZero N] {Φ : ZMod N → ℂ}, Φ 0 = 0 → ∑ j, Φ j = 0 → Differentiable ℂ (ZMod.completedLFunction Φ)Special case of differentiableAt_completedLFunction asserting differentiability everywhere
under suitable hypotheses.
- Defined in
- Mathlib.NumberTheory.LSeries.ZMod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- ZModstatement and proof · cited by 1,024
- Differentiablestatement · cited by 298
- ZMod.completedLFunctionstatement · cited by 14
- ZMod.differentiableAt_completedLFunctionproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ZMod.completedLFunction_one_sub_oddproof · cited by 1