Year: 2026
Type: article
Abstract: For an irrational alpha element of double struck upper R α ∈ R $\alpha\in {{\mathbb{R}}}$ and any beta element of double struck upper R β ∈ R $\beta\in {{\mathbb{R}}}$ , we consider additive problems with the set of primes satisfying StartMetric alpha p plus beta EndMetric less than or equals 1 divided by p Superscript tau ‖ α p + β ‖ ≤ 1 / p τ $\left\lVert\alpha p+\beta\right\rVert\leq {1}/{p^\tau}$ for some fixed tau greater than 0 τ > 0 $\tau\gt0$ . In particular, we show that there exist infinitely many non-trivial three-term arithmetic progressions in the set of primes satisfying StartMetric alpha p plus beta EndMetric less than or equals 1 divided by p Superscript tau ‖ α p + β ‖ ≤ 1 / p τ $\left\lVert\alpha p+\beta\right\rVert\leq {1}/{p^\tau}$ for tau element of left parenthesis 0 comma 1 divided by 8 right parenthesis τ ∈ ( 0 , 1 / 8 ) $\tau\in(0, 1/8)$ . We also consider a binary Goldbach-type problem.
Author: SARVAGYA JAIN
Institution: University of Turku
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Funder: Turun Yliopisto
OpenAlex ID: W4414460351
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