| Summary: | Two number fields K and L are said to be Arf equivalent if there exists a bijection T : Ω<sub>K</sub> → Ω<sub>L</sub> of places of K and of L such that K<sub>P</sub> and L<sub>TP</sub> are locally Arf equivalent for every place P ε Ω<sub>K</sub>. That is, |K<sup>*</sup><sub>p</sub>/K<sup>*2</sup><sub>p</sub>| = |L<sup>*</sup><sub>TP</sub>/L<sup>*2</sup><sub>TP</sub>|, type[( , )<sub>P</sub>] = type[( , )<sub>TP</sub>], and Arf(r<sub>P</sub> ) = Arf(r<sub>TP</sub> ) for every place P ε Ω<sub>K</sub>,
where r<sub>P</sub> is the local Artin root number function and ( , )<sub>P</sub> is the Hilbert symbol on K<sup>*</sup><sub>p</sub>. In this dissertation, an infinite set of quadratic number fields are classified up to Arf equivalence.
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