Some New Applications of the Subspace Theorem |
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Authors: | Pietro Corvaja Umberto Zannier |
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Institution: | (1) Dipartimento di Mat. e Inf., via delle Scienze, 206, 33100 Udine, Italy;(2) IUAV – DCA, S. Croce, 191, 30135 Venice, Italy |
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Abstract: | 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(q
n
) is an algebraic integer for infinitely many n, then h(f(q
n
)) 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. |
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Keywords: | Subspace Theorem Mahler's series Exponential diophantine equations |
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