تقرير
Relations alg\'ebriques entre valeurs de E-fonctions ou de M-fonctions
العنوان: | Relations alg\'ebriques entre valeurs de E-fonctions ou de M-fonctions |
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المؤلفون: | Adamczewski, Boris, Faverjon, Colin |
سنة النشر: | 2023 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Number Theory, 11J91, 11J81 (Primary) 11B85 (Secondary) |
الوصف: | We prove that all algebraic relations over $\overline{\mathbb Q}$ between values of Siegel's $E$-functions at some non-zero algebraic point have a functional source, in that they can be obtained as degeneration of $\delta$-algebraic relations over $\overline{\mathbb Q}(z)$ between the functions at stake. We also obtain an analogous result when considering Mahler's $M_q$-functions. In this case, the so-called $\sigma_q$-algebraic relations substitute for the $\delta$-algebraic relations. We also give several consequences of this result concerning some descent phenomena. The point of view we adopt here reveals some striking similarities between the theory of $E$-functions and the one of $M_q$-functions. Comment: in French language |
نوع الوثيقة: | Working Paper |
اللغة: | French |
URL الوصول: | http://arxiv.org/abs/2303.05997 |
رقم الأكسشن: | edsarx.2303.05997 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |