Binary Hermitian forms over a cyclotomic field

2009/01/21 by Dan Yasaki, Yasaki, Dan
Mathematics · #11H55 #53C35 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0901.3346

openalex publication_date 2009/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let z be a primitive fifth root of unity and let F be the cyclotomic field F=Q(z). Let O be the ring of integers. We compute the Voronoi polyhedron of binary Hermitian forms over F and classify GL₂(O)-conjugacy classes of perfect forms. The combinatorial data of this polyhedron can be used to compute the cohomology of the arithmetic group GL₂(O) and Hecke eigen forms.

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