Prime-representing functions and Hausdorff dimension

K. Saito

doi:10.1007/s10474-021-01170-6

Prime-representing functions and Hausdorff dimension

K. Saito

Nagoya University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let c≥ 2 be any fixed real number. Matomäki [4] inverstigated the set of A> 1 such that the integer part of Ack is a prime number for every k∈ N. She proved that the set is uncountable, nowhere dense, and has Lebesgue measure 0. In this article, we show that the set has Hausdorff dimension 1.

Original language	English
Pages (from-to)	203-217
Number of pages	15
Journal	Acta Mathematica Hungarica
Volume	165
Issue number	1
DOIs	https://doi.org/10.1007/s10474-021-01170-6
Publication status	Published - Oct 2021
Externally published	Yes

Keywords

distribution of prime numbers
Hausdorff dimension
prime-representing function

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10.1007/s10474-021-01170-6

Cite this

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KW - Hausdorff dimension

KW - prime-representing function

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Prime-representing functions and Hausdorff dimension

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Keywords

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