Irrationality of Power Series for Various Number Theoretic Functions

This is a preprint of an article published in Manuscripta Mathmatica (2005), Volume 117, Number 2, 183-197. DOI: 10.1007/s00229-005-0564-3. The final publication is available at springerlink.com.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