Variations on a Theme of Mirsky
No Thumbnail Available
Date
2023
Authors
Akbal, Yıldırım
Güloǧlu,A.M.
Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific
Open Access Color
OpenAIRE Downloads
OpenAIRE Views
Abstract
Let k and r be non-zero integers with r ≥ 2. An integer is called r-free if it is not divisible by the rth power of a prime. A result of Mirsky states that there are infinitely many primes p such that p + k is r-free. In this paper, we study an additive Goldbach-type problem and prove two uniform distribution results using these primes. We also study certain properties of primes p such that p + a1,...,p + aℓ are simultaneously r-free, where a1,...,aℓ are non-zero integers and ℓ ≥ 1. © 2023 World Scientific Publishing Company.
Description
AKBAL, YILDIRIM/0000-0003-2138-4050
ORCID
Keywords
Goldbach-type additive problems, Hardy-Littlewood circle method, r -free shifted primes
Turkish CoHE Thesis Center URL
Fields of Science
Citation
0
WoS Q
Q3
Scopus Q
Q3
Source
International Journal of Number Theory
Volume
19
Issue
1
Start Page
1
End Page
39