Date of Award

1989

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Robert V. Perlis

Abstract

The author studies reciprocity equivalence and the wild set of a reciprocity equivalence. He proves that if two algebraic number fields K and L are reciprocity equivalent then there exists a reciprocity equivalence between them with an infinite wild set. In particular, there always exists a self-equivalence with an infinite wild set on any algebraic number field. Even though a wild set of an equivalence can be infinite, he proves that its Dirichlet density is always zero. The structure of a reciprocity equivalence is examined. He proves that the bijection on primes determines the group isomorphism on global square classes in an equivalence. Indeed he proves more. Namely, if (t$\sb1,T\sb1$) and (t$\sb2,T\sb2$) are reciprocity equivalences from K to L and the bijections T$\sb1$ and T$\sb2$ on primes agree on a set of Dirichlet density bigger than zero, then the global square class group isomorphisms t$\sb1$ and t$\sb2$ agree everywhere, and T$\sb1$ agrees with T$\sb2$ at every noncomplex prime.

Pages

35

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