
TL;DR
This paper applies Green's transference principle to demonstrate that dense subsets of prime powers contain solutions to certain linear equations, providing explicit bounds and extending understanding of additive properties of primes.
Contribution
It introduces a novel application of Green's transference principle to prime powers, establishing solutions to linear equations with explicit quantitative bounds.
Findings
Dense subsets of prime powers contain solutions to translation-invariant linear equations.
Explicit bounds are provided for the solutions.
The method extends additive number theory techniques to prime powers.
Abstract
We use Green's transference principle to show that any subset of the th powers of primes with positive relative density contains nontrivial solutions to a translation-invariant linear equation in or more variables, with explicit quantitative bounds.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
