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Density Theorems for Reciprocity Equivalences.

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 equi­ valence whose wild set is infinite. Theorem C: Given (t, T), the bijection T determines the global square class isomorphism t.