`gTerm` is homogeneous of degree `-3`
ProvedBlockCycleRotation.gTerm_smulanalytic-number-theoryblock-cycle-rotationzeta-values
gTerm is homogeneous of degree -3.
This is an auxiliary lemma of the formalization rather than a result stated in the paper. It is used in the proof of tsum_gTerm_eq.
Preamble
import Definitions.Def_BlockCycleRotation_Remark21 import Mathlib open BlockCycleRotation open Real Finset Filter Topology
Formal statement
theorem BlockCycleRotation.gTerm_smul {k a a' : ℕ} (hk : 0 < k) (h1 : 1 ≤ a') (h2 : a' < a) :
gTerm (k * a, k * a') = gTerm (a, a') / (k : ℝ) ^ 3 := by sorrySource
Valentin Blomer and Kai-Uwe Bux, "The cost of cyclic permutations and remainder sums in the Euclidean algorithm", AofA 2026, LIPIcs vol. 381, pp. 14:1-14:17, doi:10.4230/LIPIcs.AofA.2026.14. Numbering follows the full version, arXiv:2601.00979v1. Lean source: https://github.com/dbenbenn/block-cycle-rotation/blob/f69003fd8b00c9b5d6d1a4f6807b4943bce0a92c/BlockCycleRotation/Remark21.lean#L223-L240