Arithmetical Functions, Code Theory and Distribution properties of the Residual Order
| Project/Area Number |
21540027
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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 | Meiji Gakuin University |
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Principal Investigator |
MURATA Leo 明治学院大学, 経済学部, 教授 (30157789)
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| Co-Investigator(Kenkyū-buntansha) |
CHINEN Koji 近畿大学, 理工学部, 准教授 (30419486)
KAMIYA Yuichi 大東文化大学, 経済学部, 講師 (90553412)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 解析的整数論 / 数論的関数 / Code 理論 / 剰余位数 / code / paper-folding sequence / Code理論 / Sum of diits function / Automaton / 一般剰余類群 / 一般剩余類群 / Gray Code / Sum of digits function |
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| Research Abstract |
From a code C, we can define the “sum of digits function” f_C(n), usually f_C(n) fluctuates quite irregularly. In this research, we proved “a one-to-one correspondence between arithmetical functions and the sum of digits function of code C’s”. This result enables us to control complex sum-of-digits functions by simple arithmetical functions. As an application, we can obtain the Delange-type average of sum-of-digits function of Gray code. We alsoconsider relations between sum-of-digits function and Automaton etc.
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Report
(4 results)
Research Products
(17 results)
