论文标题
全球磁场整数环的多项式，它们具有根部模拟每个有限索引子组
Polynomials over Ring of Integers of Global Fields that have Roots Modulo Every Finite Indexed Subgroup
论文作者
论文摘要
整数环中具有系数的多项式$ \ Mathcal {o} _ {k} $的全局字段$ k $，如果它具有root modulo的每个有限索引子组的$ \ Mathcal {O} _} _ {k} $。我们证明了两个多项式$ f（x）\ in \ mathcal {o} _ {k} [x] $相互作用的标准。这些标准之一是根据多项式分裂字段的Galois组，而第二个标准完全可以完全根据依赖$ k $和多项式$ f $的常数来验证。证明使用全球场扩展理论，在Chebotarev密度定理中最不优势的上限。
A polynomial with coefficients in the ring of integers $\mathcal{O}_{K}$ of a global field $K$ is called intersective if it has a root modulo every finite-indexed subgroup of $\mathcal{O}_{K}$. We prove two criteria for a polynomial $f(x)\in\mathcal{O}_{K}[x]$ to be intersective. One of these criteria is in terms of the Galois group of the splitting field of the polynomial, whereas the second criterion is verifiable entirely in terms of constants which depend upon $K$ and the polynomial $f$. The proofs use the theory of global field extensions and upper bound on the least prime ideal in the Chebotarev density theorem.
