Variations on a theme of Mirsky
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Date
2023
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Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific Publ Co Pte Ltd
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.
Description
AKBAL, YILDIRIM/0000-0003-2138-4050
Keywords
Hardy-Littlewood circle method, r-free shifted primes, Goldbach-type additive problems
Turkish CoHE Thesis Center URL
Citation
0
WoS Q
Q3
Scopus Q
Q3
Source
Volume
19
Issue
1
Start Page
1
End Page
39