Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2106.06084 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911330032680960 |
|---|---|
| author | Schmidt, Matthew |
| author_facet | Schmidt, Matthew |
| contents | We present a new determinant identity involving the coefficients of the Artin-Hasse exponential. In particular, if $E(x) = \exp(\sum_{k=0}^\infty \frac{x^{p^k}}{p^k}) = \sum_{n=0}^\infty u_nx^n$ is the Artin-Hasse exponential, we give, for any $\ell\geq 1$, a closed-form formula for the determinant $|u_{pi-j}|_{1\leq i,j\leq \ell}$ and show it is a $p$-adic unit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_06084 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A determinant of the Artin-Hasse exponential coefficients Schmidt, Matthew Number Theory We present a new determinant identity involving the coefficients of the Artin-Hasse exponential. In particular, if $E(x) = \exp(\sum_{k=0}^\infty \frac{x^{p^k}}{p^k}) = \sum_{n=0}^\infty u_nx^n$ is the Artin-Hasse exponential, we give, for any $\ell\geq 1$, a closed-form formula for the determinant $|u_{pi-j}|_{1\leq i,j\leq \ell}$ and show it is a $p$-adic unit. |
| title | A determinant of the Artin-Hasse exponential coefficients |
| topic | Number Theory |
| url | https://arxiv.org/abs/2106.06084 |