关于Perlis和Stuart关于算术等价的一个问题
On a question of Perlis and Stuart regarding arithmetic equivalence
摘要：
设$K$为数字字段。有理素数$\ell$的$K$ -算术类型是$K$中$\ell$的剩余度的元组$A_{K}(\ell)=(f^{K}_{1},...,f^{K}_{g_{\ell}})$，以升序书写。一个众所周知的结果玻璃从70年代的国家，两个数字领域有相同戴德金ζ函数当且仅当几乎所有的素数$\ell$的算术类型的$\ell$在这两个领域一致。到90年代末，Perlis和Stuart问是否具有相同的Zeta函数意味着分歧素数的分歧度之和一致。在这里，我们研究和回答他们的问题，脓毒症号码字段。
英文摘要：
Let $K$ be a number field. The $K$-arithmetic type of a rational prime $\ell$ is the tuple $A_{K}(\ell)=(f^{K}_{1},...,f^{K}_{g_{\ell}})$ of the residue degrees of $\ell$ in $K$, written in ascending order. A well known result of Perlis from the 70's states that two number fields have the same Dedekind zeta function if and only if for almost all primes $\ell$ the arithmetic types of $\ell$ in both fields coincide. By the end of the 90's Perlis and Stuart asked if having the same zeta function implies that for ramified primes the sum of the ramification degrees coincide. Here we study and answer their question for septic number fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
