2013 Fiscal Year Final Research Report
Application of continued fractions to real quadratic fields
| Project/Area Number |
22540030
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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 | Gakushuin University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TOMITA Koshi 名城大学, 理工学部, 准教授 (50300207)
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| Co-Investigator(Renkei-kenkyūsha) |
KISHI Yasuhiro 愛知教育大学, 教育学部, 准教授 (60380375)
SUZUKI Hiroshi 名古屋大学, 大学院多元数理科学研究科, 准教授 (70235993)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | ガウス予想 / 類数 / 基本単数 / 連分数 / 極小型実二次体 / 極小型自然数 / 末尾急増型主要対称部分 / 増殖分解 |
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| Research Abstract |
(1) Kawamoto-Tomita(2012) posed a conjecture by using numerical datas that the minimal element of each period gives a real quadratic field with class number 1 of minimal type. (2) We examine to construct such a field in each even period, and then Kawamoto-Kishi-Tomita(2014) gave a way of constructing positive integers with even period of minimal type. (3) By using this construction, we introduce notions of ``extremely large end (ELE)'' for a primary symmetric part and of ``pre-ELE type'' for a finite string. Then we give a way of constructing primary symmetric parts of ELE type. (4) Moreover, we introduce a notion of ``a growth decomposition'' for a finite string of pre-ELE type, and then give a way of constructing finite strings of pre-ELE type. As a byproduct, we show that there exist infinitely many real quadratic fields of minimal type in each period which is even and greater than or equal to 6.
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Research Products
(7 results)
