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
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
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