Irrationality of power series for various number theoretic functions

William D. Banks*, Florian Luca, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)183-197
Number of pages15
JournalManuscripta Mathematica
Volume117
Issue number2
DOIs
Publication statusPublished - Jun 2005

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