# Minimal redundant digit expansions in the gaussian integers

Journal de théorie des nombres de Bordeaux (2002)

- Volume: 14, Issue: 2, page 517-528
- ISSN: 1246-7405

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topHeuberger, Clemens. "Minimal redundant digit expansions in the gaussian integers." Journal de théorie des nombres de Bordeaux 14.2 (2002): 517-528. <http://eudml.org/doc/248905>.

@article{Heuberger2002,

abstract = {We consider minimal redundant digit expansions in canonical number systems in the gaussian integers. In contrast to the case of rational integers, where the knowledge of the two least significant digits in the “standard” expansion suffices to calculate the least significant digit in a minimal redundant expansion, such a property does not hold in the gaussian numbers : We prove that there exist pairs of numbers whose non-redundant expansions agree arbitrarily well but which have different least significant digits in minimal redundant expansions.},

author = {Heuberger, Clemens},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {minimal redundant expansions; Gaussian integers},

language = {eng},

number = {2},

pages = {517-528},

publisher = {Université Bordeaux I},

title = {Minimal redundant digit expansions in the gaussian integers},

url = {http://eudml.org/doc/248905},

volume = {14},

year = {2002},

}

TY - JOUR

AU - Heuberger, Clemens

TI - Minimal redundant digit expansions in the gaussian integers

JO - Journal de théorie des nombres de Bordeaux

PY - 2002

PB - Université Bordeaux I

VL - 14

IS - 2

SP - 517

EP - 528

AB - We consider minimal redundant digit expansions in canonical number systems in the gaussian integers. In contrast to the case of rational integers, where the knowledge of the two least significant digits in the “standard” expansion suffices to calculate the least significant digit in a minimal redundant expansion, such a property does not hold in the gaussian numbers : We prove that there exist pairs of numbers whose non-redundant expansions agree arbitrarily well but which have different least significant digits in minimal redundant expansions.

LA - eng

KW - minimal redundant expansions; Gaussian integers

UR - http://eudml.org/doc/248905

ER -

## References

top- [1] C. Heuberger, H. Prodinger, On minimal expansions in redundant number systems: Algorithms and quantitative analysis. Computing66 (2001), 377-393. Zbl1030.11003MR1842756
- [2] I. Kátai, J. Szabó, Canonical number systems for complex integers. Acta Sci. Math. (Szeged) 37 (1975), 255-260. Zbl0309.12001MR389759
- [3] D.E. Knuth, Seminumerical algorithms, third ed. The Art of Computer Programming, vol. 2, Addison-Wesley, 1998. Zbl0895.65001MR633878
- [4] B. Kovács, A. Pethö, Number systems in integral domains, especially in orders of algebraic number fields. Acta Sci. Math.(Szeged) 55 (1991), 287-299. Zbl0760.11002MR1152592

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