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 fractionnairesArticle
Authors: Michel Balazard 1; Leila Benferhat
2; Mihoub Bouderbala 2 NULL##0000-0001-6802-738X##NULL
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 :∑n≥0|{x/(n+a)}−{x/(n+b)}|=2πζ(3/2)√cx+O(c2/9x4/9),
with
c=b−a, uniformly for
x≥40c−5(1+b)27/2.
Volume: Volume 29 (2021), Issue 3
Published on: December 23, 2021
Imported on: May 11, 2022
Keywords: Elementary methods,Fractional part,van der Corput estimates,MSC classification : 11N37,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Funding:
Source : OpenAIRE Graph- Incentive - LA 3 - 2013; Code: Incentivo/SAU/LA0003/2013