Kronecker Constants of Arithmetic Progressions
| Autor: | L. Thomas Ramsey, Kathryn E. Hare |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Experimental Mathematics. 23:414-422 |
| ISSN: | 1944-950X 1058-6458 |
| DOI: | 10.1080/10586458.2014.928656 |
| Popis: | We prove that for every positive integer d and for all θ ∈ {0, 1/2}d − 1, there is at least one real number x such that where ⟨u⟩ is the distance from u to the set of integers. The bound 1/2 − 1/d is best possible and is necessary for θ = (1/2, …, 1/2). Consequently, the angular Kronecker constant of {1, … , d − 1} is bounded below by 1/2 − 1/d. We also exhibit a minimal (finite) set of points x such that given θ ∈ {0, 1/2}d − 1, there is some x in the set such that max n⟨θn − nx⟩ ≤ 1/2 − 1/d. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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