On Hermite’s problem, Jacobi–Perron type algorithms, and Dirichlet groups
Oleg Karpenkov
Abstract
A well-known result of Lagrange (1770) characterises quadratic irrationalities as those real numbers that can be written as periodic continued fractions. Hermite asked in 1848 if there exists some way to write cubic irrationalities periodically. To ap
Topics & Concepts
MathematicsHermite polynomialsType (biology)Quadratic equationDirichlet distributionPure mathematicsApplied mathematicsAlgebra over a fieldAlgorithmMathematical analysisGeometryBoundary value problemEcologyBiologyHistory and Theory of MathematicsAdvanced Mathematical IdentitiesAdvanced Combinatorial Mathematics