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A sum involving the greatest-integer function

Number Theory 2023-10-12 v1
Authors: David Ross Richman
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Abstract

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

Keywords

divisor function exponential sums multiplicative functions

Cite

@article{arxiv.1906.12032,
  title  = {A sum involving the greatest-integer function},
  author = {David Ross Richman},
  journal= {arXiv preprint arXiv:1906.12032},
  year   = {2023}
}

Comments

13 pages, accepted for publication in INTEGERS

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