Density theorems for reciprocity equivalences - Palfrey, Thomas C. (Annales Mathematicae Silesianae, 1998)
A reciprocity equivalence between two number fields is a Hilbert symbol preserving pair of maps (t,T), in which t is a group isomorphism between the global square class groups of the two fields, and T is a bijection between the sets of primes. For two reciprocity equivalent number fields, it is proved that: Theorem A : The Dirichlet density of the wild set of any reciprocity equivalence is zero. Theorem B: There exists a reciprocity equivalence whose wild set is infinite. Theorem C: Given (t,T), the bijection T determines the global square class isomorphism t.