Normal properties of numbers in the terms of their representation by the Perron series

• Datum: 2023
• Hauptverfasser: Moroz, M., Мороз, Микола
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2023
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/7503
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 511.7 We examine the representation of real numbers by the Perron series ($P$-representation) given by $$(0;1]\ni x=\sum\limits_{n=0}^{\infty}\frac{r_0 r_1\ldots r_n}{(p_1-1)p_1\ldots(p_n-1)p_n p_{n+1}}=\Delta^P_{p_1 p_2\ldots},\quad\mbox{where}\quad r_n,p_n\in\mathbb{N},\quad p_{n+1}\geq r_n+1,...