Trace Problems in Algebraic Number Fields and Applications to Characters of Finite Groups

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.