Abstract. Simultaneous rational approximants to a vector of functions $(f_1,\ldots,f_m)$ that forms a Nikishin system are investigated. A new error formula for the $m$-th component of the approximation error is proved. It is well known that the common denominators of the simultaneous approximants satisfy a multiple orthogonality relation; it is shown that they also satisfy an ordinary one, which allows us to prove interesting properties of the approximants. The zeros of the $m^{th}$ remainder function $R_m$ are analysed. Complementary results for the zeros of the remainder functions $R_1,\ldots, R_{m-1}$ will be published in a separate paper.

AMS Subject Classification (1991): 41A21, 30E10

Keyword(s): Nikishin systems, simultaneous rational approximants, normality, orthogonal polynomials, multiple orthogonality

Received June 13, 1994. (Registered under 5630/2009.)