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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.12139 |
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Table of Contents:
- For an irrational $α\in \mathbb{R}$, we consider additive problems with the set of primes satisfying $\lVertαp\rVert\leq \frac{1}{p^τ}$ for some fixed $τ>0$. In particular, we show that there exist infinitely many non-trivial three-term arithmetic progressions in the set of primes satisfying $\lVert αp\rVert\leq \frac{1}{p^τ}$ for $τ\in(0, \tfrac18)$. We also consider a binary Goldbach-type problem.