2011 Fiscal Year Final Research Report
Arithmetical Functions, Code Theory and Distribution properties of the Residual Order
| Project/Area Number |
21540027
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Meiji Gakuin University |
|---|
Principal Investigator |
MURATA Leo 明治学院大学, 経済学部, 教授 (30157789)
|
|---|
| 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)
|
|---|
| Project Period (FY) |
2009 – 2011
|
| Keywords | 解析的整数論 / 数論的関数 / Code 理論 / 剰余位数 |
|---|
| 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.
|
