Research Article
Squares in a Beatty sequence and an improvement on character sums
https://doi.org/10.21203/rs.3.rs-4322039/v1
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We consider the distribution of perfect squares in a Beatty sequence, which is of the form ⌊αn + β⌋. We also analyze it on average over positive square-free integers. The proof relies on a new bound of character sums with Beatty sequences, which answers an open question posted by Igor Shparlinski.
MSC Numbers: 11B83; 11L07; 11L40.
Beatty sequences
square numbers
exponential sums
character sums
No competing interests reported.
Editorial decision: Revision requested
03 Nov, 2024
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Reviewers agreed at journal
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Submission checks completed at journal
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First submitted to journal
25 Apr, 2024
You are reading this latest preprint version