Additive Problems with Primes from a Thin Bohr Set

2025/08/16 by Jain, Sarvagya
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.12139

Abstract

For an irrational α∈ ℝ, we consider additive problems with the set of primes satisfying ‖αp‖≤ (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 ‖ αp‖≤ (1)/(p^τ) for τ∈(0, \tfrac18). We also consider a binary Goldbach-type problem.

Citations

• Strong Bounds for 3-Progressions
• Piatetski-Shapiro Primes in a Beatty Sequence
• Roth's theorem in the primes
• Khintchine’s problem in metric Diophantine approximation

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• On some additive problems in number theory (v.3)
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• The ternary Goldbach problem with primes from arithmetic progressions
• 10 conjectures in additive number theory