2022 Fiscal Year Final Research Report
Self-inducing structure of arithmetic algorithms
| Project/Area Number |
17K05159
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
湯浅 久利 大阪教育大学, 教育学部, 准教授 (50363346)
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| 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 |
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| 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.
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| Free Research Field |
Number Theory
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| 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。
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