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On number system constructions

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Abstract

We investigate various number system constructions. After summarizing earlier results we prove that for a given lattice Λ and expansive matrix M: Λ → Λ if ρ(M −1) < 1/2 then there always exists a suitable digit set D for which (Λ, M, D) is a number system. Here ρ means the spectral radius of M −1. We shall prove further that if the polynomial f(x) = c 0 + c 1 x + ··· + c k x k ∈ Z[x], c k = 1 satisfies the condition |c 0| > 2 Σ k i=1 |c i | then there is a suitable digit set D for which (Z k, M, D) is a number system, where M is the companion matrix of f(x).

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Authors and Affiliations

  1. Department of Computer Algebra, Eötvös Loránd University, 1117, Budapest, Pázmány P. sétány I/C., Hungary

    L. Germán & A. Kovács

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  1. L. Germán
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  2. A. Kovács
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Additional information

The research was supported by the Number Theory Research Group of the Hungarian Academy of Sciences.

The research was supported by OTKA-T043657 and Bolyai Fellowship Committee.

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Germán, L., Kovács, A. On number system constructions. Acta Math Hung 115, 155–167 (2007). https://doi.org/10.1007/s10474-007-5224-5

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  • DOI: https://doi.org/10.1007/s10474-007-5224-5

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