THREE-TERM ARITHMETIC PROGRESSIONS OF PIATETSKI-SHAPIRO SEQUENCES (Problems and Prospects in Analytic Number Theory)
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- 齋藤, 耕太
- 名古屋大学
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説明
For every non-integral α > 1, the sequence of the integer parts of n^α (n = 1, 2, ... ) is called the Piatetski-Shapiro sequence with exponent a. Let PS(α) be the set of all those terms. In a previous study, Matsusaka and the author studied the set of α ∈ I such that PS(α) contains infinitely many arithmetic progressions of length 3, where I is a closed interval of [2, ∞). As a corollary of their main result , they showed that the set is uncountable and dense in I. The aim of this article is to provide a direct proof of this result.
収録刊行物
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- 数理解析研究所講究録
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数理解析研究所講究録 2196 1-4, 2021-08
京都大学数理解析研究所
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詳細情報 詳細情報について
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- CRID
- 1050008445609187584
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- NII書誌ID
- AN00061013
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- HANDLE
- 2433/265749
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- ISSN
- 18802818
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- 本文言語コード
- en
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB
- KAKEN