A+ CATEGORY SCIENTIFIC UNIT

Sums of reciprocals of additive functions running over short intervals

Volume 107 / 2007

J.-M. De Koninck, I. Kátai Colloquium Mathematicum 107 (2007), 317-326 MSC: 11A25, 11N37. DOI: 10.4064/cm107-2-11

Abstract

Letting $f(n)=A\log n+t(n)$, where $t(n)$ is a small additive function and $A$ a positive constant, we obtain estimates for the quantities $\sum _{x \le n \le x+H} 1/f(Q(n))$ and $\sum _{x \le p \le x+H} 1/f(Q(p))$, where $H=H(x)$ satisfies certain growth conditions, $p$ runs over prime numbers and $Q$ is a polynomial with integer coefficients, whose leading coefficient is positive, and with all its roots simple.

Authors

  • J.-M. De KoninckDépartement de mathématiques
    Université Laval
    Québec G1K 7P4, Canada
    e-mail
  • I. KátaiComputer Algebra Department
    Eötvös Loránd University
    Pázmány Péter Sétány I//C
    1117 Budapest, Hungary
    e-mail

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