Continued fraction approach to Gauss reduction theory

DOI10.1007/978-3-030-89716-1_7OpenAlexW3211012607MaRDI QIDQ2695490

Oleg N. Karpenkov

Publication date: 31 March 2023

Full work available at URL: https://arxiv.org/abs/2107.02687

zbMATH Keywords

continued fractionsinteger matricesgeometry of numbersGauss reduction theory

Mathematics Subject Classification ID

Theory of computing (68Qxx)

Cites Work

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• Determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators
• On irrational lattice angles
• When are two elements of \(GL(2,\mathbb{Z}{})\) similar?
• Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world
• Continued fractions, modular symbols, and noncommutative geometry
• Multidimensional Gauss reduction theory for conjugacy classes of \(\mathrm{SL}(n,\mathbb Z)\)
• Generalized Perron identity for broken lines
• Elementary notions of lattice trigonometry
• Reversing symmetry group of and matrices with connections to cat maps and trace maps
• Geometry of continued fractions
• Factorization and similarity in \(\text{GL}(2,\mathbb{Z})\)

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