## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  734.11047
Autor:  Erdös, Paul; Pomerance, Carl; Schmutz, Eric
Title:  Carmichael's lambda function. (In English)
Source:  Acta Arith. 58, No.4, 363-385 (1991).
Review:  Let \lambda(.) be Carmichael's function, i.e. \lambda(n) equals the l.c.m of the orders of primitive residues mod n. Using a more explicit representation via Euler's function the authors investigate the average order, normal order, and minimal order of \lambda. For example they show that for x \geq 16

1/x sumn \leq x \lambda(n) = \frac{x}{log x}\exp {\frac{B log log x}{log log log x}(1+o(1))}

holds with some explicit constant B. Some other problems connected with Euler's function are discussed.
Reviewer:  T.Maxsein (Frankfurt / Main)
Classif.:  * 11N37 Asymptotic results on arithmetic functions
11A07 Congruences, etc.
11N45 Asymptotic results on counting functions for other structures
Keywords:  asymptotic formulas; universal exponent; Carmichael's function; orders of primitive residues; Euler's function; average order; normal order; minimal order

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