Theorems · Theorem · number theory
ZLattice.summable_norm_sub_zpow
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] (L : Submodule ℤ E)
[DiscreteTopology ↥L], ∀ n < -↑(Module.finrank ℤ ↥L), ∀ (x : E), Summable fun z => ‖↑z - x‖ ^ n- Defined in
- Mathlib.Algebra.Module.ZLattice.Summable
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Submodulestatement and proof · cited by 7,192
- Norm.normstatement and proof · cited by 5,413
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- Summablestatement and proof · cited by 778
- DiscreteTopologystatement and proof · cited by 373
- Real.rpow_intCastproof · cited by 35
- ZLattice.summable_norm_sub_rpowproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- ZLattice.summable_norm_sub_inv_powproof · cited by 1
- PeriodPair.hasSum_sumInvPowproof · cited by 1
- ZLattice.summable_norm_zpowproof · cited by 0