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