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 :\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: Elementary methods,Fractional part,van der Corput estimates,MSC classification : 11N37,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]

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