Abstract.
We prove a theorem giving arbitrarily long explicit sequences \( x_{1},\ldots,x_{s} \) of algebraic numbers such that any nonzero polynomial f(X) satisfying \( f(x_{1}) = \cdots = f(x_{s}) = 0 \) has nonscalar complexity \( > C \sqrt{s} \) for some positive constant C independent of s. A similar result is shown for rapidly growing rational sequences.
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Received: April 6 1999.
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Baur, W., Halupczok, K. On lower bounds for the complexity of polynomials and their multiples. Comput. complex. 8, 309–315 (1999). https://doi.org/10.1007/s000370050001
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DOI: https://doi.org/10.1007/s000370050001