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We study the behavior of the Ozsvath-Szabo and Rasmussen knot concordanceinvariants tau and s on K(m,n), the (m,n)-cable of a knot K where m and n arerelatively prime. We show that for every knot K and for any fixed positiveinteger m, both of the invariants evaluated on K(m,n) differ from their valueon the torus knot T(m,n) by a fixed constant for all but finitely many n>0.Combining this result together with Hedden's extensive work on the behavior oftau on (m,mr+1)-cables yields bounds on the value of tau on any (m,n)-cable ofK. In addition, several of Hedden's obstructions for cables bounding complexcurves are extended.

Ozsvath-Szabo and Rasmussen invariants of cable knots