CORRESPONDING ABELIAN EXTENSIONS AND A GROUP THEORETIC APPROACH TO STRONG MULTIPLICITY ONE FOR SOME POLYNOMIAL EULER PRODUCTS

<p dir="ltr">We review arithmetic equivalence and define more general notions of arithmetic</p><p dir="ltr">similarity. We then study the arithmetic similarity of corresponding abelian exten-</p><p dir="ltr">sions of integrally equivalent number fields. This sheds some light on what one could</p><p dir="ltr">reasonably hope for in a sort of generalized Neukirch-Uchida Theorem. We finally</p><p dir="ltr">derive Strong Multiplicity One type results for certain polynomial Euler products</p><p dir="ltr">using only the rudiments of group actions. Highlights of this thesis are an extension</p><p dir="ltr">of a result due to Arapura-Katz-McReynolds-Solapurkar and an effectivization of a</p><p dir="ltr">theorem of Perlis-Stuart.</p>