Metric Heights on an Abelian Group
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2012
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908292834394112 |
|---|---|
| author | Samuels, Charles L. |
| author_facet | Samuels, Charles L. |
| contents | Suppose $m(α)$ denotes the Mahler measure of the non-zero algebraic number $α$. For each positive real number $t$, the author studied a version $m_t(α)$ of the Mahler measure that has the triangle inequality. The construction of $m_t$ is generic, and may be applied to a broader class of functions defined on any Abelian group $G$. We prove analogs of known results with an abstract function on $G$ in place of the Mahler measure. In the process, we resolve an earlier open problem stated by the author regarding $m_t(α)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1211_1890 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Metric Heights on an Abelian Group Samuels, Charles L. Number Theory 11R04, 11G50 Suppose $m(α)$ denotes the Mahler measure of the non-zero algebraic number $α$. For each positive real number $t$, the author studied a version $m_t(α)$ of the Mahler measure that has the triangle inequality. The construction of $m_t$ is generic, and may be applied to a broader class of functions defined on any Abelian group $G$. We prove analogs of known results with an abstract function on $G$ in place of the Mahler measure. In the process, we resolve an earlier open problem stated by the author regarding $m_t(α)$. |
| title | Metric Heights on an Abelian Group |
| topic | Number Theory 11R04, 11G50 |
| url | https://arxiv.org/abs/1211.1890 |