Additive Problems with Primes from a Thin Bohr Set
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913993872900096 |
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| author | Jain, Sarvagya |
| author_facet | Jain, Sarvagya |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12139 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additive Problems with Primes from a Thin Bohr Set Jain, Sarvagya Number Theory 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. |
| title | Additive Problems with Primes from a Thin Bohr Set |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.12139 |