Multidimensional Continued Fractions over the Field of Formal Power Series

Key Points

• The aim is to analyze multidimensional continued fraction algorithms and their diophantine properties in the context of formal power series.
• Studied algorithms related to multidimensional continued fractions
• Analyzed the properties of these algorithms over formal power series
• Compared the properties with those in the real case
• Found that the simultaneous diophantine properties are stronger in the formal power series case than in the real case
• Demonstrated key advantages of the algorithms in handling multidimensional cases