#### 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.

#### Recommended Citation

Palfrey, Thomas Carrere, "Density Theorems for Reciprocity Equivalences." (1989). *LSU Historical Dissertations and Theses*. 4799.

http://digitalcommons.lsu.edu/gradschool_disstheses/4799

#### Pages

35