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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 2

Divisor function and bounds in domains with enough primes

Haydar Göral0000-0002-8814-6295
Pages
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Publication Date
2019-04-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Then, we discuss for which rings the absolute value bound for the Bézout identity is not trivial and the answer depends on the number of small primes in the ring.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this note, first we show that there is no uniform divisor bound for the Bézout identity using Dirichlet's theorem on arithmetic progressions.
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Key Findings & Data:In this note, first we show that there is no uniform divisor bound for the Bézout identity using Dirichlet's theorem on arithmetic progressions.
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Conclusion & Impact:Then, we discuss for which rings the absolute value bound for the Bézout identity is not trivial and the answer depends on the number of small primes in the ring.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:divisor function · arithmetic progression · polynomials

Abstract

In this note, first we show that there is no uniform divisor bound for the Bézout identity using Dirichlet's theorem on arithmetic progressions. Then, we discuss for which rings the absolute value bound for the Bézout identity is not trivial and the answer depends on the number of small primes in the ring.

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Cite This Article

Göral, H. (2019). Divisor function and bounds in domains with enough primes. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 2. https://ajindex.com/articles/1402808

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