manuscripta mathematica

, Volume 117, Issue 2, pp 183–197

Irrationality of Power Series for Various Number Theoretic Functions

  • William D. Banks
  • Florian Luca
  • Igor E. Shparlinski

DOI: 10.1007/s00229-005-0564-3

Cite this article as:
Banks, W., Luca, F. & Shparlinski, I. manuscripta math. (2005) 117: 183. doi:10.1007/s00229-005-0564-3


We study formal power series whose coefficients are taken to be a variety of number theoretic functions, such as the Euler, Möbius and divisor functions. We show that these power series are irrational over ℤ[X], and we obtain lower bounds on the precision of their rational approximations.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • William D. Banks
    • 1
  • Florian Luca
    • 2
  • Igor E. Shparlinski
    • 3
  1. 1.Department of MathematicsUniversity of Missouri ColumbiaUSA
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México MoreliaMéxico
  3. 3.Department of ComputingMacquarie UniversitySydneyAustralia

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