Identifier

etd-07052006-110113

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

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.

Date

2006

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Robert Perlis

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