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Some New Applications of the Subspace Theorem

Published online by Cambridge University Press:  04 December 2007

Pietro Corvaja  and
Umberto Zannier
Pietro Corvaja
Affiliation:
Dipartimento di Mat. e Inf., via delle Scienze, 206, 33100 Udine, Italy. E-mail: corvaja@dimi.uniud.it
Umberto Zannier
Affiliation:
IUAV – DCA, S. Croce, 191, 30135 Venice, Italy. E-mail: zanier@iuav.unive.it
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Abstract

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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.

Keywords

Subspace TheoremMahler's seriesExponential diophantine equations
Type
Research Article
Information
Compositio Mathematica , Volume 131 , Issue 3 , May 2002 , pp. 319 - 340
Copyright
© 2002 Kluwer Academic Publishers