Conjugacy Classes of Hyperbolic Matrices in Sl(n, Z) and Ideal Classes in an Order

DOI10.2307/1999996zbMath0562.12010OpenAlexW4254979162MaRDI QIDQ5187368

Dorothy I. Wallace

Publication date: 1984

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1999996

zbMATH Keywords

unitseigenvaluesbijectionideal classesnarrow ideal classesGL(n,\({\mathbb{Z}})\)-conjugacy classeshyperbolic SL(n,\({\mathbb{Z}})\)-matricesSL(n,\({\mathbb{Z}})\)-conjugacy classessubring of algebraic integers

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Eigenvalues, singular values, and eigenvectors (15A18) Iwasawa theory (11R23) Class numbers of quadratic and Hermitian forms (11E41) Matrices of integers (15B36) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (6)

Explicit form of the hyperbolic term in the Selberg trace formula for \(Sl(3,{\mathbb{Z}})\) and Pell's equation for hyperbolics in \(Sl(3,{\mathbb{Z}})\) ⋮ Arithmeticity of groups $mathbb{Z}^n times mathbb{Z}$ ⋮ Maximal parabolic terms in the Selberg trace formula for SL(3,\({\mathbb{Z}})\backslash SL(3,{\mathbb{R}})/SO(3,{\mathbb{R}})\) ⋮ Matrix zeros of quadratic equations ⋮ ON CLASS NUMBER ONE FOR THE REAL QUADRATIC FIELD ⋮ Convex-compact subgroups of the Goeritz group

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