Variations on a theme of Mirsky
International Journal of Number Theory, cilt.19, sa.1, ss.1-39, 2023 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 19 Sayı: 1
- Basım Tarihi: 2023
- Doi Numarası: 10.1142/s179304212350001x
- Dergi Adı: International Journal of Number Theory
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Sayfa Sayıları: ss.1-39
- Anahtar Kelimeler: Goldbach-type additive problems, Hardy-Littlewood circle method, r -free shifted primes
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- TED Üniversitesi Adresli: Evet
Özet
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.