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Convergence of improper Iwasawa continued fractions.
- Source :
-
International Journal of Number Theory . Mar2024, Vol. 20 Issue 2, p299-326. 28p. - Publication Year :
- 2024
-
Abstract
- We prove the convergence of a wide class of continued fractions, including generalized continued fractions over quaternions and octonions. Fractional points in these systems are not bounded away from the unit sphere, so that the iteration map is not uniformly expanding. We bypass this problem by analyzing digit sequences for points that converge to the unit sphere under iteration, expanding on previous methods of Dani–Nogueira. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CONTINUED fractions
*CAYLEY numbers (Algebra)
*QUATERNIONS
Subjects
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 20
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 175679291
- Full Text :
- https://doi.org/10.1142/S1793042124500155