On sums of primes from Beatty sequences
On sums of primes from Beatty sequences
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发表时间：
2007-06
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通讯作者：
A. Kumchev
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作者：
A. Kumchev
设$k \ge 2$和$\alpha_1, \beta_1, ..., \alpha_k, \beta_k$为实数，使得$\alpha_i$是无理数且大于1。进一步假设某个比率$\alpha_i/\alpha_j$是不合理的。我们以$$ p_1 + p_2 + ... + p_k = n, $$的形式研究整数$n$的表示，其中$p_i$是Beatty序列中的素数 $$ \mathcal B_i = \left\{n \in \mathbb N : n = [ \alpha_i m + \beta_i ] \text{for some} m \in \mathbb Z \right\}. $$
Let $k \ge 2$ and $\alpha_1, \beta_1, ..., \alpha_k, \beta_k$ be reals such that the $\alpha_i$'s are irrational and greater than 1. Suppose further that some ratio $\alpha_i/\alpha_j$ is irrational. We study the representations of an integer $n$ in the form $$ p_1 + p_2 + ... + p_k = n, $$ where $p_i$ is a prime from the Beatty sequence $$ \mathcal B_i = \left\{n \in \mathbb N : n = [ \alpha_i m + \beta_i ] \text{for some} m \in \mathbb Z \right\}. $$