An application of Kronecker's theorem to rational functions

Universal Taylor series

“…II, p. 178). For works related to the above theorem the reader is referred to [5], [6], [7], [14], [8], [9], [15].…”

“…ith Aj e C, \pj | = 1, the partial sums SN (z) , N = 0,1,2,... of the Taylor development of uj belong to L (z) for all z, \z\ = 1, up to a finite set (see [9]). …”

Distribution of Partial Sums of the Taylor Development of Rational Functions

“…We suppose that the sequence S" -Yf=\cjQ" > n = 0> 1,..., converges to zero. There are several proofs of Lemma 2 (see [6,11]); the proof given here is due to N. Alikakos.…”