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A sum involving the greatest-integer function

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2019Embargo end date: 01 Jan 2019Publisher:arXivJournal:Integers, volume 19
Authors: Richman, D.R.;

doi: 10.48550/arxiv.1906.12032 , 10.5281/zenodo.10709780

arXiv: 1906.12032

A sum involving the greatest-integer function

Abstract

We determine properties of the set of values of $ [nx] - ([x]/1 + [2x]/2 + \cdots + [nx]/x) $ as $n$ and $x$ vary.

13 pages, accepted for publication in INTEGERS

Keywords

Mathematics - Number Theory, 26D15 (Primary), 40A25, 11A99 (Secondary), Arithmetic functions; related numbers; inversion formulas, FOS: Mathematics, Inequalities for sums, series and integrals, Number Theory (math.NT), greatest-integer function

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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