2013 Fiscal Year Final Research Report
Analytic, Algebraic and Combinatorial studies on continued fractions
| Project/Area Number |
22540005
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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 | Hirosaki University |
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Principal Investigator |
KOMATSU Takao 弘前大学, 理工学研究科, 教授 (70300556)
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| Co-Investigator(Renkei-kenkyūsha) |
MUNEMASA Akihiro 東北大学, 大学院情報科学研究科, 教授 (50219862)
AKIYAMA Shigeki 筑波大学, 大学院数理物質科学研究科, 教授 (60212445)
TANAKA Takaaki 慶応義塾大学, 理工学部, 講師 (60306850)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 数論 / 代数学 / 組み合わせ論 / 連分数 |
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| Research Abstract |
Analytic studies of continued fractions are to obtain exact algebraic expressions for approximation evalucations of various Hurwitz and Tasoev continued fractions, some relations between Fibonacci-zeta functions and continued fractions, and some relations between zeta functions and Cauchy polynomials. Algebraic studies of continued fractions are to obtain independence measures of arithmetic functions and to construct Liouville numbers in non- Archimedean case. Combinatorial studies of continued fractions are to give upper bounds on cyclotomic numbers, and to discover linear recurrence relations associated with multinomial Pascal triangles. In addition, cross-studies of continued fractions are to show some relations among continued fractions, Fibonacci numbers and congruent numbers, and to discover the concept of poly Cauchy numbers and polynomials as some generalizations of Cauchy numbers, which are related with Bernoulli numbers.
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