Trace Problems in Algebraic Number Fields and Applications to Characters of Finite Groups
Stan, Florin
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https://hdl.handle.net/2142/86912
Description
Title
Trace Problems in Algebraic Number Fields and Applications to Characters of Finite Groups
Author(s)
Stan, Florin
Issue Date
2008
Doctoral Committee Chair(s)
Zaharescu, Alexandru
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
In the second chapter, we define the Siegel norm of algebraic numbers, and study it in connection to the spectral norm. In the last section of the chapter we compute its values on a large class of elements of Q ≃ , the completion of Q&d1; with respect to the spectral norm. The third chapter concerns Kedlaya's conjecture on m-Weil numbers. We introduce the notion of unitary conductor, and prove the conjecture for cyclotomic integers with square-free unitary conductor.
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