Finite $A_2$-continued fractions in the problems of rational approximations of real numbers:

• Datum: 2023
• Hauptverfasser: Pratsiovytyi, M., Goncharenko, Ya., Lysenko, I., Ratushniak, S., Працьовитий, Микола, Гончаренко, Яніна, Лисенко, Ірина, Ратушняк, Софія
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2023
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/7413
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 511.7+517.5 We consider finite continued fractions whose elements are numbers  $\dfrac{1}{2}$ and $1$ (the so-called $A_2$-continued fractions): $1/a_1+1/a_2+\ldots+1/a_n=[0;a_1,a_2,\ldots,a_n],$ $a_i\in A_2=\left\{\dfrac{1}{2},1\right\}.$ We study the stru...