Continued fraction expansions for complex numbers-a general approach

• Autorzy: S. G. Dani
• Języki publikacji: EN

Abstrakty

EN

We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the absolute values of the denominators of the convergents for a class of continued fraction algorithms with partial quotients in the ring of Eisenstein integers.

Kategorie tematyczne

• 11J25: Diophantine inequalities
• 11J70: Continued fractions and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 171
• Numer: 4
• Strony: 355-369

Daty

wydano

2015

Twórcy

autor

S. G. Dani

• Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

Identyfikatory

DOI

10.4064/aa171-4-4