论文标题
Prime K-tuples的一种变体，并应用于量子限制
A variation of the prime k-tuples conjecture with applications to quantum limits
论文作者
论文摘要
令$ \ MATHCAL {H}^{*} = \ {H_1，H_2，\ ldots \} $是整数的有序集。 We give sufficient conditions for the existence of increasing sequences of natural numbers $a_j$ and $n_k$ such that $n_k+h_{a_j}$ is a sum of two squares for every $k\geq 1$ and $1\leq j\leq k.$ Our method uses a novel modification of the Maynard-Tao sieve together with a second moment estimate.作为我们结果的一种特殊情况，我们根据D. jakobson提出了一个猜想，这对Flat Tori的量子限制具有几个影响。
Let $\mathcal{H}^{*}=\{h_1,h_2,\ldots\}$ be an ordered set of integers. We give sufficient conditions for the existence of increasing sequences of natural numbers $a_j$ and $n_k$ such that $n_k+h_{a_j}$ is a sum of two squares for every $k\geq 1$ and $1\leq j\leq k.$ Our method uses a novel modification of the Maynard-Tao sieve together with a second moment estimate. As a special case of our result, we deduce a conjecture due to D.~Jakobson which has several implications for quantum limits on flat tori.
