In this paper, we generalize the result of Fouvry and Iwaniec dealing with prime values of the quadratic form $x^2+y^2$ with one input restricted to a thin subset of the integers. We prove the same result with an arbitrary primitive positive definite binary quadratic form. In particular, for any positive definite binary quadratic form $F$ and binary linear form $G$, there exist infinitely many $\ell ,m\in \mathbb{Z}$ such that both $F(\ell ,m)$ and $G(\ell ,m)$ are primes as long as there are no local obstructions.

中文翻译：

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具有稀薄变量的二进制二次形式的素值

在本文中，我们推广了Fouvry和Iwaniec处理二次形式的素值的结果 $X^2+{ÿ}^2$一个输入限制为整数的一小部分。我们用任意原始正定二进制二次形式证明了相同的结果。特别是对于任何正定二进制二次形式$F$ 和二进制线性形式 $G$，无限地存在 $\ell ，米\in \mathbb{ž}$ 这样 $F（\ell ，米）$ 和 $G（\ell ，米）$ 只要没有局部障碍物，它们就是素数。