On the singularities of differential equations satisfied by $E$-functions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914498371125248 |
|---|---|
| author | Fischler, Stéphane Rivoal, Tanguy |
| author_facet | Fischler, Stéphane Rivoal, Tanguy |
| contents | Let $ξ$ be a value, at an algebraic point, of a Siegel $E$-function. As a special case of a very general interpolation result, we prove that there exists an $E$-function $f$ such that $f(1)=ξ$, and such that 1 is not a singularity of the minimal differential equation satisfied by $f$. We prove that the same property does not hold at the point $0$, when $ξ$ is the value at a non-zero algebraic number of the Bessel function. This answers an analogue of a question asked by Yves Andr{é} for $G$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the singularities of differential equations satisfied by $E$-functions Fischler, Stéphane Rivoal, Tanguy Number Theory Let $ξ$ be a value, at an algebraic point, of a Siegel $E$-function. As a special case of a very general interpolation result, we prove that there exists an $E$-function $f$ such that $f(1)=ξ$, and such that 1 is not a singularity of the minimal differential equation satisfied by $f$. We prove that the same property does not hold at the point $0$, when $ξ$ is the value at a non-zero algebraic number of the Bessel function. This answers an analogue of a question asked by Yves Andr{é} for $G$-functions. |
| title | On the singularities of differential equations satisfied by $E$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.20332 |