Multidimensional integer trigonometry

DOI10.46298/cm.10919MaRDI QIDQ6594635

James G. Dolan, John Blackman, Oleg Karpenkov

Publication date: 28 August 2024

Published in: Communications in Mathematics (Search for Journal in Brave)

zbMATH Keywords

best approximationslattice geometrymultidimensional Euclidean algorithms

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Lattices and convex bodies (number-theoretic aspects) (11H06) Continued fractions (11A55)

Cites Work

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• Über vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Veränderlichen. (On four-dimensional Riemann surfaces of many-valued analytic functions of two complex variables)
• On irrational lattice angles
• Higher dimensional analogues of periodic continued fractions and cusp singularities
• Darstellung der Funktionen eines algebraischen Körpers zweier unabhängigen Veränderlichen \(x, y\) in der Umgebung \(=a,\;y= b\).
• On a geometric representation of the development into regular continued fractions
• Continued fractions, modular symbols, and noncommutative geometry
• Generalised Markov numbers
• Zwei Sätze über inhomogene diophantische Approximation von Irrationalzahlen
• Elementary notions of lattice trigonometry
• Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix
• On Hermite’s problem, Jacobi–Perron type algorithms, and Dirichlet groups
• Geometry of continued fractions

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Euclidean lattices: theory and applications

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