Michel Balazard ; Leila Benferhat ; Mihoub Bouderbala - Sur la variation de certaines suites de parties fractionnaires

cm:9553 - Communications in Mathematics, December 23, 2021, Volume 29 (2021), Issue 3 - https://doi.org/10.2478/cm-2020-0021
Sur la variation de certaines suites de parties fractionnairesArticle

Authors: Michel Balazard 1; Leila Benferhat ORCID2; Mihoub Bouderbala 2

  • 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 :n0|{x/(n+a)}{x/(n+b)}|=2πζ(3/2)cx+O(c2/9x4/9),

with c=ba, uniformly for x40c5(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

Classifications

Mathematics Subject Classification 20201

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