Continued fractions for complex numbers and values of binary quadratic forms

DOI10.1090/S0002-9947-2014-06003-0zbMath1392.11006arXiv1102.3754OpenAlexW2090987657MaRDI QIDQ5420126

Arnaldo Nogueira, Shrikrishna G. Dani

Publication date: 11 June 2014

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

Full work available at URL: https://arxiv.org/abs/1102.3754

Mathematics Subject Classification ID

Quadratic forms over global rings and fields (11E12) Continued fractions (11A55) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Noncompact transformation groups (22Fxx)

Related Items (20)

Sets of exact approximation order by complex rational numbers ⋮ The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms ⋮ The geometry of Gaussian integer continued fractions ⋮ A Method of Determining of Switching Instants for Discrete-Time Control Systems ⋮ Calculations of the Invariant Measure for Hurwitz Continued Fractions ⋮ On the ergodic theory of maps associated with the nearest integer complex continued fractions over imaginary quadratic fields ⋮ Diophantine exponents for standard linear actions of ${\rm SL}_2$ over discrete rings in $\mathbb {C}$ ⋮ Geodesic Gaussian integer continued fractions ⋮ On sums of partial quotients in Hurwitz continued fraction expansions ⋮ Singular vectors on manifolds over totally real number fields ⋮ Convergence of improper Iwasawa continued fractions ⋮ Purely periodic and transcendental complex continued fractions ⋮ Good’s theorem for Hurwitz continued fractions ⋮ The Farey octahedron graph, the Poincaré polyhedron theorem and Gaussian integer continued fractions ⋮ On the construction of the natural extension of the Hurwitz complex continued fraction map ⋮ A complex Borel-Bernstein theorem ⋮ Finite Partitions for Several Complex Continued Fraction Algorithms ⋮ Necessary and sufficient conditions for convergence of integer continued fractions ⋮ THE DIFFERENCE BETWEEN THE HURWITZ CONTINUED FRACTION EXPANSIONS OF A COMPLEX NUMBER AND ITS RATIONAL APPROXIMATIONS ⋮ From binary Hermitian forms to parabolic cocycles of Euclidean Bianchi groups

Cites Work

• On orbits of \(\text{SL}(2,\mathbb Z)_{+}\) and values of binary quadratic forms on positive integral pairs
• Diophantine approximation of complex numbers
• The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions
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