The transcendence of $\mathrm{e}$ via formal power series
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917492775976960 |
|---|---|
| author | Klazar, Martin |
| author_facet | Klazar, Martin |
| contents | We review Hilbert's classical analytical proof of the transcendence of the number $\mathrm{e}$. Then, we show how this result can be obtained algebraically by means of formal power series (FPS). We give two proofs of the transcendence of $\mathrm{e}$ based on FPS. The first of them is a specialization of the 1990 proof by Beukers, Bézivin and Robba of the Lindemann-Weierstrass theorem. The second proof is due to this author and is an adaptation of Hilbert's argument to FPS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01019 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The transcendence of $\mathrm{e}$ via formal power series Klazar, Martin Number Theory We review Hilbert's classical analytical proof of the transcendence of the number $\mathrm{e}$. Then, we show how this result can be obtained algebraically by means of formal power series (FPS). We give two proofs of the transcendence of $\mathrm{e}$ based on FPS. The first of them is a specialization of the 1990 proof by Beukers, Bézivin and Robba of the Lindemann-Weierstrass theorem. The second proof is due to this author and is an adaptation of Hilbert's argument to FPS. |
| title | The transcendence of $\mathrm{e}$ via formal power series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.01019 |