| Title:
|
Mahler measures in a cubic field (English) |
| Author:
|
Dubickas, Artūras |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
949-956 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that every cyclic cubic extension $E$ of the field of rational numbers contains algebraic numbers which are Mahler measures but not the Mahler measures of algebraic numbers lying in $E$. This extends the result of Schinzel who proved the same statement for every real quadratic field $E$. A corresponding conjecture is made for an arbitrary non-totally complex field $E$ and some numerical examples are given. We also show that every natural power of a Mahler measure is a Mahler measure. (English) |
| Keyword:
|
Mahler measure |
| Keyword:
|
Pisot numbers |
| Keyword:
|
cubic extension |
| MSC:
|
11R06 |
| MSC:
|
11R09 |
| MSC:
|
11R16 |
| idZBL:
|
Zbl 1164.11068 |
| idMR:
|
MR2261666 |
| . |
| Date available:
|
2009-09-24T11:39:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128119 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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|
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| . |
