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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

On the fractional part of the sum and product of two p-adic β-integers 

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pp. 1–13Online FirstMay 2026DOI: 10.47974/JIM-2224XML
Received:
01 Oct 2024
Published Online:
12 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2224
Pages:
1–13

Abstract

This paper aims to explore arithmetic properties in the set of p-adic β-integers. We show that the quantities Lʘ and L⊕ are finite if β is an algebraic integer of odd degree. Here, Lʘ (resp. L⊕) denotes the largest shift after the decimal point in the product (resp. sum) of two β-integers when this shift is finite.

Keywords

Subject Classifications

11R0637B50

References

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