2013 Fiscal Year Final Research Report
Multidimensional continued fraction algorithm
| Project/Area Number |
22540037
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Toho University (2012-2013)
Suzuka National College of Technology (2010-2011) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TAMURA Jun-ichi 津田塾大学, 付置研究所, 研究員 (90418905)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 連分数 / 単数 / 高次元連分数 |
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| Research Abstract |
We were able to suggest a new class of multidimensional continued fraction algorithms, which improve our algorithms that we have studied. The numerical experiments support the extension of classical results of the Lagrange theorem
for the number field of degree less than 7 and the generation of fundamental units in number fields of degree less than 5. We have fundamental results about the relation between the class of algorithms and substitutions on two dimensional stepped surfaces.
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Research Products
(13 results)
