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Harald Bohr’s work in the early twentieth century (Bohr in Math Phys Klasse 441–488, 1913 [14]) made crucial contributions to the development of a comprehensive theory of Dirichlet series. He explored the connection between Dirichlet series and power series in infinitely many variables, which led him to consider whether the absolute values of the coefficients of such series could be compared. This observation gave rise to what is now known as Bohr’s inequality. This paper reviews recent developments of the Bohr inequality, focusing mainly on the bounds of Bohr radius for specific power series within the unit ball of finite-dimensional Banach sequence spaces.

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Survey on the Bohr Radius in Higher Dimension

  • 会议论文

  • 发表日期：

    2026年

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  • Shankey Kumar,
  • Saminathan Ponnusamy

摘要

Harald Bohr’s work in the early twentieth century (Bohr in Math Phys Klasse 441–488, 1913 [14]) made crucial contributions to the development of a comprehensive theory of Dirichlet series. He explored the connection between Dirichlet series and power series in infinitely many variables, which led him to consider whether the absolute values of the coefficients of such series could be compared. This observation gave rise to what is now known as Bohr’s inequality. This paper reviews recent developments of the Bohr inequality, focusing mainly on the bounds of Bohr radius for specific power series within the unit ball of finite-dimensional Banach sequence spaces.