论文标题
由无限的单基因族产生的代数数字字段
Algebraic number fields generated by an infinite family of monogenic trinomials
论文作者
论文摘要
For an infinite family of monogenic trinomials $P(X) = X^3\pm 3rbX-b$ in $\mathbb{Z}\lbrack X\rbrack$, arithmetical invariants of the cubic number field $L = \mathbb{Q}(θ)$, generated by a zero $θ$ of $P(X)$, and of its Galois closure确定$ n = l（\ sqrt {d（l）}）$。周期性立方相对扩展的导体$ f $，其中$ k = \ mathbb {q}（\ sqrt {d（l）}）$表示$ n $的唯一二次次级子场，被证明是$ 3^eb $ in \ lbrace $ e \ lbrace $ lbrace $ lbrace $ lbrace 1,2 ebrace cans cans cans cans cans cans cans $ 3^eb $ cans cans cans cans cans cans cans cans cans cans cans cans cans 1,2 2，22理想，晶格最小值和$ L $的独立单位。确定$ ldots，ldots，l_m $的数字$ m $ $ ldots $ ldots $ $ $ $ $ $ $ $共享一个常见的判别$ d（l_i）= d（l）$ a $ l $。
For an infinite family of monogenic trinomials $P(X) = X^3\pm 3rbX-b$ in $\mathbb{Z}\lbrack X\rbrack$, arithmetical invariants of the cubic number field $L = \mathbb{Q}(θ)$, generated by a zero $θ$ of $P(X)$, and of its Galois closure $N = L(\sqrt{d(L)})$ are determined. The conductor $f$ of the cyclic cubic relative extension $N/K$, where $K = \mathbb{Q}(\sqrt{d(L)})$ denotes the unique quadratic subfield of $N$, is proved to be of the form $3^eb$ with $e\in\lbrace 1,2\rbrace$, which admits statements concerning primitive ambiguous principal ideals, lattice minima, and independent units in $L$. The number $m$ of non-isomorphic cubic fields $L_1,\ldots,L_m$ sharing a common discriminant $d(L_i) = d(L)$ with $L$ is determined.
