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Effective simultaneous approximation of complex numbers by conjugate algebraic integers by G. J. Rieger (Hannover) We study effectively the simultaneous approximation of n − 1 different complex numbers by conjugate algebraic integers of degree n over Z( √−1). This is a refinement of a result of Motzkin [2] (see also [3], p. 50) who has no estimate for the remaining conjugate. If the n−1 different complex numbers lie symmetrically about the real axis, then Z( √−1) can be replaced by Z. In Section 1 we prove an effective version of a Kronecker approximation theorem; we start with an idea of H. Bohr and E. Landau (see e.g. [4]); later we use an estimate of A. Baker for linear forms with logarithms. This and also Rouché’s theorem are then applied in Section 2 to give the result; the re-quired irreducibility is guaranteed by the Schönemann–Eisenstein criterion. 1. On the Kronecker approximation theorem. Let k ∈ N: = {n ∈ Z | n> 0}, v ∈ N, U ∈ R, U ≥ 1, i: = √−1, e(x): = exp(2piix) (x ∈ R); let p1 < p2 <... < pk be primes and uν ∈ Z, 0 < |uν | ≤ U, βν ∈ R (ν = 1,..., k), f(t): = 1 + e(t) + k∑ ν=