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A new definition of the density of an integer sequence

Published online by Cambridge University Press:  09 April 2009

R. R. Hall
R. R. Hall
Affiliation:
Department of Mathematics University of York Heslington, York Y01 5DD England
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Abstract

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The divisor density of an integer sequence is defined: this measures the tendency of divisors of (almost all) integers to belong to the sequence. A proof of a conjecture of Erdös is given and this is linked to some previous conjectures of the author's concerning distribution (mod 1) of functions of the divisors.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 4 , December 1978 , pp. 487 - 500
Copyright
Copyright © Australian Mathematical Society 1978

References

Hall, R. R. (1974a), ‘Halving an estimate obtained from Selberg's upper bound method’, Acta Arith. 25, 347–351.CrossRefGoogle Scholar
Hall, R. R. (1974b), ‘The divisors of integers 1’, Acta Arith. 26, 41–46.CrossRefGoogle Scholar
Hall, R. R. (1976), ‘The distribution of f(d) (mod 1)’, Acta Arith. 31, 91–97.CrossRefGoogle Scholar
Hardy, G. H. (1948), Divergent series (Oxford).Google Scholar
Titchmarsh, E. C. (1951), The theory of the Riemann Zeta function (Oxford).Google Scholar
Wirsing, E. (1967), ‘Das asymptotische Verhalten von summen über multiplikative Functionen II’, Acta Math. Acad. Sci. Hung. 18, 411–467.CrossRefGoogle Scholar