论文标题
罗斯的定理和hardy-稀薄子集的小木材主要问题
Roth's Theorem and the Hardy--Littlewood majorant problem for thin subsets of primes
论文作者
论文摘要
我们引入了零相对密度的素数的一系列确定性基集，并在这些集合中证明了罗斯定理，即，我们表明，其任何呈正相对上层密度的任何子集都包含许多无限的非平凡的三项算术算术进度。我们还证明，硬木 - 小木马物业适用于这些素数。值得注意的是，我们的考虑因素恢复了piatetski-shapiro Prime的结果，用于接近$ 1 $，这是固定$ c> 1 $的$ \ lfloor n^c \ rfloor $的素质。
We introduce a wide class of deterministic subsets of primes of zero relative density and we prove Roth's Theorem in these sets, namely, we show that any subset of them with positive relative upper density contains infinitely many non-trivial three-term arithmetic progressions. We also prove that the Hardy--Littlewood majorant property holds for these subsets of primes. Notably, our considerations recover the results for the Piatetski--Shapiro primes for exponents close to $1$, which are primes of the form $\lfloor n^c\rfloor$ for a fixed $c>1$.
