Relations algébriques entre valeurs de $E$-fonctions ou de $M$-fonctions
We show that all algebraic relations over $\overline{\mathbb{Q}}$ between the values of Siegel $E$-functions at non-zero algebraic points have a functional origin, in the sense that they can be obtained by degeneracy of algebro-differential relations over $\overline{\mathbb{Q}}(z)$ between the funct...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-11-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.634/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We show that all algebraic relations over $\overline{\mathbb{Q}}$ between the values of Siegel $E$-functions at non-zero algebraic points have a functional origin, in the sense that they can be obtained by degeneracy of algebro-differential relations over $\overline{\mathbb{Q}}(z)$ between the functions under consideration. We obtain a similar result for the Mahler $M_q$-functions, in which the algebro-differential relations are replaced by the $\sigma _q$-algebraic relations. We also give several consequences of this result, in particular with respect to certain descent phenomena. The point of view adopted reveals striking similarities between the theory of $E$-functions and that of $M_q$-functions. |
|---|---|
| ISSN: | 1778-3569 |