Michel Balazard ; Leila Benferhat ; Mihoub Bouderbala
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Sur la variation de certaines suites de parties fractionnaires
cm:9553 -
Communications in Mathematics,
December 23, 2021,
Volume 29 (2021), Issue 3
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https://doi.org/10.2478/cm-2020-0021Sur la variation de certaines suites de parties fractionnairesArticleAuthors: Michel Balazard
1; Leila Benferhat
2; Mihoub Bouderbala
2
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Michel Balazard;Leila Benferhat;Mihoub Bouderbala
- 1 Institut de Mathématiques de Marseille
- 2 Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]
Let $b > a > 0$. We prove the following asymptotic formula :\begin{equation*}\sum_{n\ge 0} \big\lvert\{x/(n+a)\}-\{x/(n+b)\}\big\rvert=\frac{2}{\pi}\zeta(3/2)\sqrt{cx}+O(c^{2/9}x^{4/9}),\\\end{equation*}with $c=b-a$, uniformly for $x \ge 40 c^{-5}(1+b)^{27/2}$.
Volume: Volume 29 (2021), Issue 3
Published on: December 23, 2021
Imported on: May 11, 2022
Keywords: MSC classification : 11N37, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], [en] Elementary methods, Fractional part, van der Corput estimates
Funding:
Source : OpenAIRE Graph- Incentive - LA 3 - 2013; Code: Incentivo/SAU/LA0003/2013