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Prime-representing functions and Hausdorff dimension
- Publication Year :
- 2021
-
Abstract
- In 2010, Matom��ki investigated the set of $A>1$ such that the integer part of $ A^{c^k} $ is a prime number for every $k\in \mathbb{N}$, where $c\geq 2$ is any fixed real number. 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 $1$.<br />15 pages
- Subjects :
- Lebesgue measure
Mathematics - Number Theory
General Mathematics
Nowhere dense set
Prime number
Metric Geometry (math.MG)
Prime (order theory)
Combinatorics
Integer
Mathematics - Metric Geometry
Hausdorff dimension
FOS: Mathematics
Uncountable set
Number Theory (math.NT)
Real number
Mathematics
Primary:11K55, Secondary:11A41
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9a1621d8742a83bed6a9562e91899f1f