Functiones et Approximatio Commentarii Mathematici

Sur les dilatations entières de la fonction partie fractionnaire

Michel Balazard

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Résumé

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). $

Abstract

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). $

Article information

Source
Funct. Approx. Comment. Math., Volume 35 (2006), 37-49.

Dates
First available in Project Euclid: 16 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229442615

Digital Object Identifier
doi:10.7169/facm/1229442615

Mathematical Reviews number (MathSciNet)
MR2271605

Zentralblatt MATH identifier
1196.11117

Subjects
Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses

Keywords
Hilbert space fractional part

Citation

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


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