Title page for ETD etd-07052006-110113


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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