Analytic, Algebraic and Combinatorial studies on continued fractions

连分数的解析、代数和组合研究

• 批准号: 22540005
• 负责人: KOMATSU Takao
• 金额: $ 2.58万
• 依托单位: Hirosaki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540005/
• 关键词: 数論; 代数学; 組み合わせ論; 連分数; 整数論; 組合せ論; 線形関係式; Leaping convergents

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.

持续分数的分析研究是为了获得精确的代数表达式，以进行各种Hurwitz和Tasoev的近似评估，持续的分数，斐波那酸ZETA函数与持续分数之间的某些关系，以及Zeta函数与cauchy dolynorials之间的某些关系。对持续分数的代数研究是为了获得算术功能的独立性度量，并在非阿基米德案例中构建了liouville数字。持续分数的组合研究是为了在环形数字上给出上限，并发现与多项式Pascal三角形相关的线性复发关系。此外，持续分数的交叉研究将显示持续的分数，斐波那契数和一致数量之间的某些关系，并发现poly cauchy数字和多项式的概念是与伯诺利数字有关的库奇数字的某些概括。

项目成果

HYPERGEOMETRIC CAUCHY NUMBERS

• DOI: 10.1142/s1793042112501473
• 发表时间: 2013-04
• 期刊: International Journal of Number Theory
• 影响因子: 0.7
• 作者: T. Komatsu

Four-term leaping recurrence relations

四项跳跃递推关系

• 发表时间: 2009
• 期刊: 数理解析研究所講究録 1639
• 作者: Takao Komatsu;Carsten Elsner;Iekata Shiokawa;Takao Komatsu;Takao Komatsu
• 通讯作者: Takao Komatsu

Independence measures of arithmetic functions II

算术函数的独立性测度 II

• 发表时间: 2012
• 期刊: Acta Arith.
• 作者: Takao Komatsu;V. Laohakosol and P. Ruengsinsub
• 通讯作者: V. Laohakosol and P. Ruengsinsub

Sums of products of Cauchy numbers, including poly-Cauchy numbers

柯西数的乘积和，包括聚柯西数

• 发表时间: 2013
• 期刊: J. Discrete Math.
• 作者: J.C.Eilbeck;S.Matustani;Y.Onishi;Takao Komatsu;Y.Onishi;Takao Komastsu
• 通讯作者: Takao Komastsu

On the nearest integer of the sum of reciprocal Fibonacci numbers

关于斐波那契数倒数之和的最接近整数

• 发表时间: 2010
• 作者: Hacene Belbachir;Takao Komatsu;Laszlo Szalay;小松尚夫;Takao Komatsu;Takao Komatsu;Takao Komatsu;Takao Komatsu;Takao Komatsu;小松 尚夫;Takao Komatsu;Takao Komatsu;Takao Komatsu;T. Komatsu;K. Kamano and T. Komatsu;Takao Komatsu;Takao Komatsu;Takao Komatsu;Takao Komatsu;T. Komatsu;T. Komatsu;T. Komatsu;T. Komatsu;T. Komatsu;T. Komatsu;T. Komatsu;Takao Komatsu;小松尚夫;小松尚夫;Takao Komatsu;Takao Komatsu;Takao Komatsu;T. Komatsu;T. Komatsu;T. Komatsu;Takao Komatsu;小松尚夫;Takao Komatsu;Takao Komatsu
• 通讯作者: Takao Komatsu