Polynomial-exponential equations -- some new cases of solvability
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912046725988352 |
|---|---|
| author | Mantova, Vincenzo Masser, David |
| author_facet | Mantova, Vincenzo Masser, David |
| contents | Recently Brownawell and the second author proved a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure". Here we treat some significant new cases. In particular these settle completely the problem of solving polynomial-exponential equations in two complex variables. The methods of proof are also new, as is the consequence, for example, that there are infinitely many complex $z$ with $e^z+e^{1/z}=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05592 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polynomial-exponential equations -- some new cases of solvability Mantova, Vincenzo Masser, David Complex Variables Logic Number Theory 03C60, 14H42, 30C15 (Primary) 32A60, 33E05, 12L12 (Secondary) Recently Brownawell and the second author proved a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure". Here we treat some significant new cases. In particular these settle completely the problem of solving polynomial-exponential equations in two complex variables. The methods of proof are also new, as is the consequence, for example, that there are infinitely many complex $z$ with $e^z+e^{1/z}=1$. |
| title | Polynomial-exponential equations -- some new cases of solvability |
| topic | Complex Variables Logic Number Theory 03C60, 14H42, 30C15 (Primary) 32A60, 33E05, 12L12 (Secondary) |
| url | https://arxiv.org/abs/2303.05592 |