Doctor of Philosophy (PhD)
Two number fields K and L are said to be Arf equivalent if there exists a bijection T : ΩK → ΩL of places of K and of L such that KP and LTP are locally Arf equivalent for every place P ε ΩK. That is, |K*p/K*2p| = |L*TP/L*2TP|, type[( , )P] = type[( , )TP], and Arf(rP ) = Arf(rTP ) for every place P ε ΩK, 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.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Kim, Jeonghun, "Classifying quadratic number fields up to Arf equivalence" (2006). LSU Doctoral Dissertations. 3198.