On some arithmetic properties of Mahler functions
| Autor: | Sara Checcoli, Julien Roques |
|---|---|
| Přispěvatelé: | Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Rolland, Ariane |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Power series
Polynomial (hyperelastic model) General Mathematics 010102 general mathematics Natural number [MATH] Mathematics [math] 0102 computer and information sciences 01 natural sciences Integer 010201 computation theory & mathematics Linear independence 0101 mathematics Algebraic number Algebra over a field Arithmetic [MATH]Mathematics [math] ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Israël Journal of Mathematics Israël Journal of Mathematics, The Hebrew University Magnes Press, 2018, 228 (2), pp.801-833 Israël Journal of Mathematics, Hebrew University Magnes Press, 2018, 228 (2), pp.801-833 |
| ISSN: | 0021-2172 1565-8511 |
| Popis: | Mahler functions are power series f(x) with complex coefficients for which there exist a natural number n and an integer l ≥ 2 such that f(x), f(xl),..., $$f({x^{{\ell ^{n - 1}}}}),f({x^{{\ell ^n}}})$$ are linearly dependent over ℂ(x). The study of the transcendence of their values at algebraic points was initiated by Mahler around the’ 30s and then developed by many authors. This paper is concerned with some arithmetic aspects of these functions. In particular, if f(x) satisfies f(x) = p(x)f(xl) with p(x) a polynomial with integer coefficients, we show how the behaviour of f(x) mirrors on the polynomial p(x). We also prove some general results on Mahler functions in analogy with G-functions and E-functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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