Short notes

The generalized Oppenheim expansions for the direct product of non-Archimedean fields

I. Y. Sukharev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The well-known Oppenheim expansion algorithm in the field $\mathbb{Q}_p$ is generalized to the ring $\mathbb{Q}_g$, where $g=p_1\cdot\ldots\cdot p_{N}$. The metric properties of the digits of this expansion and also the metric properties of the coefficients of some expansions of polyadic numbers are studied.

Key words: Oppenheim expansion, $p$-adic numbers, polyadic numbers.

UDC: 511.37+511.36

Received: 18.10.2010

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