Year: 2026
Type: article
Abstract: Denote by Φ 𝑚 (𝑋, 𝑌 ) ∈ ℤ[𝑋, 𝑌 ], 𝑚 ⩾ 1 the sequence of binary cyclotomic forms, so that Φ 𝑚 (𝑇 , 1) ∈ ℤ[𝑇 ], 𝑚 ⩾ 1 is the sequence of cyclotomic polynomials.We prove that, for 𝑚 ⩾ 3, the fundamental domainof Φ 𝑚 is a convex subset of ℝ 2 if and only if 𝑚 is equal to 𝑝, 2𝑝, or 2 𝑘 with 𝑝 an odd prime and 𝑘 ⩾ 2. Finally we investigate the convexity of the fundamental domains attached to some products of binary forms Φ 𝑚 .
Authors: Étienne Fouvry, Michel Waldschmidt
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7214683028