let $f$ be a finite extension of $bbb q$‎, ‎${bbb q}_p$ or a global‎ ‎field of positive characteristic‎, ‎and let $e/f$ be a galois extension‎. ‎we study the realization fields of‎ ‎finite subgroups $g$ of $gl_n(e)$ stable under the natural‎ ‎operation of the galois group of $e/f$‎. ‎though for sufficiently large $n$ and a fixed‎ algebraic number field $f$ every its finite extension $e$ is‎ ‎re...

An algebraic integer is said large if all its real or complex embeddings have absolute value larger than [Formula: see text]. integral ideal it admits a generator. We investigate the notion of largeness, relating to some arithmetic invariants field involved, such as regulator and covering radius lattice units. also study connection with Weil height Bogomolov property. provide an algorithm for t...

c © W W L Chen, 1984, 2013. This chapter originates from material used by the author at Imperial College London between 1981 and 1990. It is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, this document may not be kept on any information storage an...

Algebraic integers have been proven beneficial to DFT and nonrecursive FIR filter designs [2, 4] since algebraic integers can be dense in C , resulting in short word width, high speed designs. This paper uses another property of algebraic integers: algebraic integers can produce exact pole zero cancellation pairs that are used in recursive FIR, frequency sampling filter designs.