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Product Bases for the Rationals

Published online by Cambridge University Press:  20 November 2018

P. Berrizbeitia  and
P. D. T. A. Elliott
P. Berrizbeitia
Affiliation:
Departamento de Matemáticas, Universidad Simón Bolívar, Apartado 8900, Caracas 1080-A, Venezuela
P. D. T. A. Elliott
Affiliation:
Department of Mathematics, University of Colorado at Boulder Boulder, Colorado 80309-0395 U.S.A.
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Abstract

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A sequence of positive rationals generates a subgroup of finite index in the multiplicative positive rationals, and group product representations by the sequence need only a bounded number of terms, if and only if certain related sequences have densities uniformly bounded from below.

Keywords

11N9911N05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 4 , 01 December 1999 , pp. 441 - 444
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Berrizbeitia, P. and Elliott, P. D. T. A., On products of shifted primes. Ramanujan J. 2 (1998), 219–223.Google Scholar
[2] Elliott, P. D. T. A., The multiplicative group of rationals generated by the shifted primes, I. J. Reine Angew. Math. 463 (1995), 169–216.Google Scholar
[3] Ruzsa, I. Z., General Multiplicative Functions. Acta Arith. 32 (1977), 313–347.Google Scholar
[4] Wirsing, E., Das asymptotische Verhalten von Summen ¨uber multiplicative Funktionen II. Acta Math. Acad. Sci. Hungar. 18 (1967), 411–467.Google Scholar