Theorems · Theorem · number theory

ZLattice.summable_norm_rpow

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] (L : Submodule ℤ E)
  [DiscreteTopology ↥L], ∀ r < -↑(Module.finrank ℤ ↥L), Summable fun z => ‖z‖ ^ r

If L is a ℤ-lattice with rank d in E, then ∑ z ∈ L, ‖z‖ʳ converges when r < -d.

Defined in

Mathlib.Algebra.Module.ZLattice.Summable

Cited by

4 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceFiniteDimensionalDiscreteTopology