Self-inducing structure of arithmetic algorithms
| Project/Area Number |
17K05159
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
湯浅 久利 大阪教育大学, 教育学部, 准教授 (50363346)
|
|---|
| Project Period (FY) |
2017-04-01 – 2023-03-31
|
| Project Status |
Completed (Fiscal Year 2022)
|
| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | ピゾ数 / 自己相似構造 / 自己誘導構造 / Bernoulli convolution / Sarnak conjecture / normal numbers / rational number system / corona limit / タイリング / コロナ極限 / 正規数 / 生成点 / Pisot 数 / 置換規則 / 一様分布 / メビウス直交性 / 力学系 / アルゴリズム |
|---|
| Outline of Final Research Achievements |
We were able to advance research on a wide range of topics related to dynamical systems with self-similar structures. Here we list major achievements: Garcia entropy calculation algorithm of Bernoulli convolution, Self-similar structures corresponding to rational-based number systems, Moebius orthogonality of strong frequency sequences, a strong aperiodic tiling consisting of one type of tile in hyperbolic space, corona limit in a general framework and investigate its fundamental properties, normality in number theory from the point of view of dynamical systems: piecewise linear map Pisot slopes having identical generic points.
|
| Academic Significance and Societal Importance of the Research Achievements |
成果は査読付きの数学の専門誌に掲載された。これらの一般化の方向で共同研究は引き続き行われている。コロナ極限については研究方向が定まり、非周期タイル張りの場合に関心が向かっている。Bernoulli 畳み込みについては、代数的パラメータについての世界的に多くの研究が進んでいる。Sarnak 予想についても多くの関連研究が次々に発表されている。
|
Report
(7 results)
Research Products
(46 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Journal Article] On Nearly Linear Recurrence Sequences2017
Author(s)
Akiyama Shigeki, Evertse Jan-Hendrik, Pethoe Attila
-
Journal Title
Number Theory, Diophantine Problems, Uniform Distribution and Applications
Volume: -
Pages: 1-24
DOI
ISBN
9783319553566, 9783319553573
Related Report
Peer Reviewed / Int'l Joint Research
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
