Constructive Proof of Two Characterizations of Arithmetic Equivalence

Abstract

We prove a formula governing the combinatorics of cyclic group actions and extend a lemma of Hasse to account for ramification. Consequently, we obtain the first constructive proofs of two theorems characterizing arithmetic equivalence. We are also able to give new proofs of strong multiplicity one type theorems for Kronecker equivalence and weak Kronecker equivalence.