manuscripta mathematica

, Volume 117, Issue 2, pp 183–197

Irrationality of Power Series for Various Number Theoretic Functions


    • Department of MathematicsUniversity of Missouri
  • Florian Luca
    • Instituto de MatemáticasUniversidad Nacional Autónoma de México
  • Igor E. Shparlinski
    • Department of ComputingMacquarie University

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.

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© Springer-Verlag Berlin Heidelberg 2005