Classifying Quadratic Number Fields up to Arf Equivalence

by Kim, Jeonghun

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