论文标题
二次场的算术算术
Pair arithmetical equivalence for quadratic fields
论文作者
论文摘要
给定两个不同的数字字段$ k $和$ m $，以及有限的订单hecke字符$ $ k $和$ m $的$η$ $ m $，我们说$（χ，k）$和$（η，m）$在偶然上是偶然的，如果相关的l功能是相等的，如果相关的l功能：加斯曼（Gassman）在1926年进行了相同的Dedekind Zeta功能的领域问题减少了，他们发现了这类学位180的领域，以及Perlis（1977）和其他人（1977年）和其他人，他们表明没有非同义领域的学位低于$ 7 $。 我们构建了许多这样的对二次二次的对对。这给出了由不同二次场的特征引起的二面体自动形式。我们还为示例的二次字段的顺序2的此类字符进行分类，所有这些字段均具有奇数类号码。
Given two distinct number fields $K$ and $M$, and finite order Hecke characters $χ$ of $K$ and $η$ of $M$ respectively, we say that the pairs $(χ, K)$ and $(η, M)$ are arithmetically equivalent if the associated L-functions coincide: $$L(s, χ, K) = L(s, η, M) .$$ When the characters are trivial, this reduces to the question of fields with the same Dedekind zeta function, investigated by Gassman in 1926, who found such fields of degree 180, and by Perlis (1977) and others, who showed that there are no nonisomorphic fields of degree less than $7$. We construct infinitely many such pairs where the fields are quadratic. This gives dihedral automorphic forms induced from characters of different quadratic fields. We also give a classification of such characters of order 2 for the quadratic fields of our examples, all with odd class number.
