New York Journal of Mathematics
Volume 25 (2019), 558-573


Guillermo Mantilla-Soler

On a question of Perlis and Stuart regarding arithmetic equivalence

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Published: July 15, 2019.
Keywords: Arithmetic equivalence, Septic fields.
Subject: 11R42.

Let K be a number field. The K-arithmetic type of a rational prime l is the tuple AK(l)=(fK1,...,fKgl) of the residue degrees of l 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 l the arithmetic types of l 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 a nontrivial and interesting class of cases.



Author information

Guillermo Mantilla-Soler:
Department of Mathematics
Universidad Konrad Lorenz
Bogotá, Colombia