Type of Document	Dissertation
Author	Kim, Jeonghun
URN	etd-07052006-110113
Title	Classifying Quadratic Number Fields up to Arf Equivalence
Degree	Doctor of Philosophy (Ph.D.)
Department	Mathematics
Advisory Committee	Advisor Name Title Robert Perlis Committee Chair Bogdan Oporowski Committee Member Gestur Olafsson Committee Member Jurgen Hurrelbrink Committee Member Richard A. Litherland Committee Member Jerry Trahan Dean's Representative
Keywords	Arf equivalence local root numbers quadratic number fields
Date of Defense	2006-05-10
Availability	unrestricted
Abstract 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.
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