Smooth numbers with few nonzero binary digits

We use bounds of character sums and some combinatorial arguments to show the abundance of very smooth numbers which also have very few nonzero binary digits.

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 67; no. 1; pp. 74 - 89
Main Authors Hauck, Maximilian, Shparlinski, Igor E.
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.03.2024
Cambridge University Press
Subjects
Binary digits
Combinatorial analysis
Mathematical functions
Prime numbers
11N25
11L40
sparse binary representations
11A63
Smooth integers
character sums
Online AccessGet full text
ISSN0008-4395
1496-4287
1496-4287
DOI10.4153/S0008439523000504

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Summary:We use bounds of character sums and some combinatorial arguments to show the abundance of very smooth numbers which also have very few nonzero binary digits.
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ISSN:0008-4395
1496-4287
1496-4287
DOI:10.4153/S0008439523000504