Irrationality of Power Series for Various Number Theoretic Functions | Zendy

William D. Banks | Zendy; Florian Luca | Zendy; Igor E. Shparlinski | Zendy

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Irrationality of Power Series for Various Number Theoretic Functions

Author(s) -

William D. Banks,

Florian Luca,

Igor E. Shparlinski

Publication year - 2005

Publication title -

manuscripta mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.752

H-Index - 46

eISSN - 1432-1785

pISSN - 0025-2611

DOI - 10.1007/s00229-005-0564-3

Subject(s) - mathematics , number theory , series (stratigraphy) , power series , irrational number , euler's formula , divisor (algebraic geometry) , variety (cybernetics) , irrationality , formal power series , rational function , euler number (physics) , power (physics) , arithmetic function , pure mathematics , algebra over a field , mathematical analysis , statistics , rationality , geometry , paleontology , backward euler method , discretization , semi implicit euler method , physics , quantum mechanics , political science , law , biology

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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