Abstract: | Zolotarev polynomials are the polynomials that have minimaldeviation from zero on –1, 1] with respect to the norm||xn – xn–1 + an–2 xn–2 + ... + a1x+ an|| for given and for all ak . This note complements the paper of F. Pehersforfer J. LondonMath. Soc. (1) 74 (2006) 143–153] with exact (not asymptotic)construction of the Zolotarev polynomials with respect to thenorm L1 for | | < 1 and with respect to the norm L2 for | | 1 in the form of Bernstein–Szegö orthogonal polynomials.For all in L1 and L2 norms, the Zolotarev polynomials satisfyexactly (not asymptotically) the triple recurrence relationof the Chebyshev polynomials. |