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Additive problems with smooth integers

Volume 175 / 2016

H. Ki, H. Maier, A. Sankaranarayanan Acta Arithmetica 175 (2016), 301-319 MSC: Primary 11P55; Secondary 11N25. DOI: 10.4064/aa8205-9-2016 Published online: 30 September 2016

Abstract

We study the number $R_s(n)$ of representations of a positive integer $n$ $(\le X)$ in the form $n=m^2+l$ where $m$ is a natural number and $l$ is a $Y$-smooth integer. An analogous problem is also discussed for the number $R_p(n)$ of representations of $n \ (\le X)$ in the form $n = p+l$ where $p$ is a prime number and $l$ is again a $Y$-smooth number.

Authors

  • H. KiDepartment of Mathematics
    Yonsei University
    Seoul 03722, Korea
    and
    Korea Institute for Advanced Study
    Seoul, Korea
    e-mail
  • H. MaierInstitute for Number Theory
    and Probability Theory
    University of Ulm
    D-89069 Ulm, Germany
    e-mail
  • A. SankaranarayananSchool of Mathematics
    TIFR
    Homi Bhabha Road
    Mumbai 400 005, India
    and
    Institute for Number Theory
    and Probability Theory
    University of Ulm
    D-89069 Ulm, Germany
    e-mail
    e-mail

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