Monatshefte für Mathematik

, Volume 144, Issue 2, pp 113–130

Oscillations of Error Terms Associated with Certain Arithmetical Functions

  • Maciej Radziejewski

DOI: 10.1007/s00605-003-0147-x

Cite this article as:
Radziejewski, M. Mh Math (2005) 144: 113. doi:10.1007/s00605-003-0147-x


We prove a general theorem on oscillatory properties of error terms associated with real arithmetical functions whose Mellin transform may have singularities with several summands containing arbitrary complex powers and logarithmic polynomials. The theorem generalizes a theorem of J. Kaczorowski and J. Pintz and is motivated by the applications to algebraic integers with factorizations of distinct lengths. An application of the theorem to the study of the Hilbert semigroup modulo 5 is presented.

2000 Mathematics Subject Classification: 11N64
Key words: Oscillations of arithmetical functions, error terms, Mellin transforms, Hilbert semigroup, factorizations of distinct lengths

Copyright information

© Springer-Verlag/Wien 2004

Authors and Affiliations

  • Maciej Radziejewski
    • 1
  1. 1.Adam Mickiewicz UniversityPoznańPoland