Best Approximations by F_p^l-Continued Fractions

2021/12/01 by Kushwaha, S., Sarma, R.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.00367

Abstract

In this article, for a certain subset X of the extended set of rational numbers, we introduce the notion of \it best X-approximations of a real number. The notion of best X-approximation is analogous to that of best rational approximation. We explore these approximations with the help of F_p^l-continued fractions, where p is a prime and l∈ℕ, we show that the convergents of the F_p^l-continued fraction expansion of a real number x satisfying certain maximal conditions are exactly the best F_p^l-approximations of x.

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