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Floor, ceiling and the space between

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04 set 2025
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Motivated by a question on the ranges of the commutators of dilated floor functions in [10], together with a related problem in [3], we investigate the precise ranges of certain generalized polynomials dependent on a real parameter. Our analysis requires non-trivial tools, including Kronecker’s approximation theorem. The results highlight sharp distinctions between irrational parameters and sub-unitary and supra-unitary rational parameters. We also propose several conjectures for the irrational and supra-unitary rational cases, supported by extensive computations in Wolfram Mathematica.

Lingua:
Inglese
Frequenza di pubblicazione:
Volume Open
Argomenti della rivista:
Matematica, Matematica generale