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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.

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Correspondence to William D. Banks.

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Banks, W., Luca, F. & Shparlinski, I. Irrationality of Power Series for Various Number Theoretic Functions. manuscripta math. 117, 183–197 (2005). https://doi.org/10.1007/s00229-005-0564-3

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  • DOI: https://doi.org/10.1007/s00229-005-0564-3

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