THREE-TERM ARITHMETIC PROGRESSIONS OF PIATETSKI-SHAPIRO SEQUENCES (Problems and Prospects in Analytic Number Theory)

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Description

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.

Journal

  • RIMS Kokyuroku

    RIMS Kokyuroku 2196 1-4, 2021-08

    京都大学数理解析研究所

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Details 詳細情報について

  • CRID
    1050008445609187584
  • NII Book ID
    AN00061013
  • HANDLE
    2433/265749
  • ISSN
    18802818
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB
    • KAKEN

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