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1 results

  • Some New Applications of the Subspace Theorem

  • Pietro Corvaja, Umberto Zannier
  • Journal:
    Compositio Mathematica / Volume 131 / Issue 3 / May 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 319-340
    Print publication:
    May 2002
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  • We present some applications of the Subspace Theorem to the investigation of the arithmetic of the values of Laurent series f(z) at S-unit points. For instance we prove that if f(qn) is an algebraic integer for infinitely many n, then h(f(qn)) must grow faster than n. By similar principles, we also prove diophantine results about power sums and transcendency results for lacunary series; these include as very special cases classical theorems of Mahler. Our arguments often appear to be independent of previous techniques in the context.