Classifying quadratic number fields up to Arf equivalence

Identifier

etd-07052006-110113

Author

Jeonghun Kim, Louisiana State University and Agricultural and Mechanical CollegeFollow

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 : ­Ω_K → Ω_­L of places of K and of L such that K_P and L_TP are locally Arf equivalent for every place P ε Ω_K. That is, |K^*_p/K^*2_p| = |L^*_TP/L^*2_TP|, type[( , )_P] = type[( , )_TP], and Arf(r_P ) = Arf(r_TP ) for every place P ε Ω_K, where r_P 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.

Recommended Citation

Kim, Jeonghun, "Classifying quadratic number fields up to Arf equivalence" (2006). LSU Doctoral Dissertations. 3198.
https://repository.lsu.edu/gradschool_dissertations/3198

Committee Chair

Robert Perlis

DOI

10.31390/gradschool_dissertations.3198