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Estimates for a remainder term associated with the sum of digits function

Published online by Cambridge University Press:  18 May 2009

D. M. E. Foster
D. M. E. Foster
Affiliation:
Mathematical Institute University of St Andrews, North Haugh, St Andrews, KY16 9SS
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If q(≥2) is a fixed integer it is well known that every positive integer k may be expressed uniquely in the form

We introduce the ‘sum of digits’ function

Both the above sums are of course finite. Although the behaviour of α(q, k) is somewhat erratic, its average behaviour is more regular and has been widely studied.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 109 - 129
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

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