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January 2006 Sur les dilatations entières de la fonction partie fractionnaire
Michel Balazard
Funct. Approx. Comment. Math. 35: 37-49 (January 2006). DOI: 10.7169/facm/1229442615

Abstract

En posant $\mathbf{e_n}(t) =\{t / n\}$ et $\mathcal{H}: = L^2(0,+\infty; t^{-2}dt)$, nous dèmontrons $\frac{6}{5} + O(n^{-1}) \leq n^2 \cdot \mathrm{dist}_{\mathcal{H}}^2 \bigl(\mathbf{e_n}, \mathrm{Vect}(\mathbf{e_1}, \dots, \mathbf{e_{n-1}})\bigr) \leq \frac{3}{4} \log n + O(1). $

With $\mathbf{e_n}(t) =\{t / n\}$ and $\mathcal{H}: = L^2(0,+\infty; t^{-2}dt)$, we prove $\frac{6}{5} + O(n^{-1}) \leq n^2 \cdot \mathrm{dist}_{\mathcal{H}}^2 \bigl (\mathbf{e_n}, \mathrm{Vect}(\mathbf{e_1}, \dots, \mathbf{e_{n-1}})\bigr) \leq \frac{3}{4} \log n + O(1). $

Citation

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Michel Balazard. "Sur les dilatations entières de la fonction partie fractionnaire." Funct. Approx. Comment. Math. 35 37 - 49, January 2006. https://doi.org/10.7169/facm/1229442615

Information

Published: January 2006
First available in Project Euclid: 16 December 2008

zbMATH: 1196.11117
MathSciNet: MR2271605
Digital Object Identifier: 10.7169/facm/1229442615

Subjects:
Primary: 11M26

Rights: Copyright © 2006 Adam Mickiewicz University

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