论文标题
idéauxPremiers全面décomposéset sommes de Newton
Idéaux premiers totalement décomposés et sommes de Newton
论文作者
论文摘要
让$ k $为一个数字字段，$ f \ in k [x] $不可约的一元多项式，其系数为$ o_k $，$ k $的整数环。我们的目标是根据$ k $ $ f $的Galois集团以及与$ f $相关的线性复发序列，有时可以表征$ o_k $ modulo的主要理想。如果$α$是$ f $的根，则该标准会给$ o_k $的主要理想表征，这些理想完全分为$ k（α）$。如果$ f $的学位至少为$ 4 $，而$ f $的Galois Group是对称组或交替组，则确实适用。
Let $K$ be a number field and $f\in K[X]$ an irreducible monic polynomial with coefficients in $O_K$, the ring of integers of $K$. We aim to enounce an effective criterion, in terms of the Galois group of $f$ over $K$ and a linear recurrence sequence associated to $f$, allowing sometimes to characterize the prime ideals of $O_K$ modulo which $f$ completely splits. If $α$ is a root of $f$, this criterion therefore gives a characterization of the prime ideals of $O_K$ which split completely in $K(α)$. It does apply if the degree of $f$ is at least $4$ and the Galois group of $f$ is the symmetric group or the alternating group.
