On small fractional parts of perturbed polynomials

Paolo Minelli*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Questions concerning small fractional parts of polynomials and pseudo-polynomials have a long history in analytic number theory. In this paper, we improve on the earlier work by Madritsch and Tichy. In particular, let f = P + φ where P is a polynomial of degree k and φ is a linear combination of functions of shape xc, c, 1 < c < k. We prove that for any given irrational ζ we have min 2 ≤ p ≤ Xpprime ζf(p)f,X-ρ(k)+, for P belonging to a certain class of polynomials and with ρ(k) > 0 being an explicitly given rational function in k.

Original languageEnglish
Pages (from-to)1669-1690
Number of pages22
JournalInternational Journal of Number Theory
Issue number8
Publication statusPublished - 1 Sep 2022


  • Diophantine approximation
  • exponential sums
  • small fractional parts

ASJC Scopus subject areas

  • Algebra and Number Theory


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