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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/119/04/0559-0566

    • Keywords

       

      Strong restrictive factor; arithmetic functions; Dirichlet series; Riemann zeta-function.

    • Abstract

       

      Let 𝜆 be a real number such that 0 < 𝜆 < 1. We establish asymptotic formulas for the weighted real moments $\sum_{n≤ x}R^𝜆(n)(1-n/x)$, where $R(n)=\prod^k_{v=1}p^{𝛼 v-1}_v$ is the Atanassov strong restrictive factor function and $n=\prod^k_{v=1}p^{𝛼 v}_v$ is the prime factorization of 𝑛.

    • Author Affiliations

       

      Andrew Ledoan1 Alexandru Zaharescu2

      1. Department of Mathematics University of Rochester, Hylan Building, Rochester, New York 14627-0138, USA
      2. Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, MC-382, 1409 W. Green Street, Urbana, Illinois 61801-2975, USA
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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