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| HAL: hal-00698706, version 1 |
| arXiv: 1205.4090 |
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| Diagonalization and Rationalization of algebraic Laurent series |
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| Boris Adamczewski 1Jason P. Bell 2 |
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| (2012) |
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| We prove a quantitative version of a result of Furstenberg and Deligne stating that the the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime $p$ the reduction modulo $p$ of the diagonal of a multivariate algebraic power series $f$ with integer coefficients is an algebraic power series of degree at most $p^{A}$ and height at most $A^2p^{A+1}$, where $A$ is an effective constant that only depends on the number of variables, the degree of $f$ and the height of $f$. This answers a question raised by Deligne. |
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| 1: | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 2: | Department of Mathematics |
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Simon Fraser University |
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| Subject | : | Mathematics/Number Theory |
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| hal-00698706, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00698706 | |
| oai:hal.archives-ouvertes.fr:hal-00698706 | |
| From: Boris Adamczewski | |
| Submitted on: Thursday, 17 May 2012 17:18:22 | |
| Updated on: Friday, 18 May 2012 08:52:12 | |
