, Volume 117, Issue 2, pp 183-197

Irrationality of Power Series for Various Number Theoretic Functions

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Abstract

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.