Families of irreducible polynomials of Gaussian periods and matrices of cyclotomic numbers
Author:
F. Thaine
Journal:
Math. Comp. 69 (2000), 16531666
MSC (1991):
Primary 11R18, 11R21, 11T22
Published electronically:
May 19, 1999
MathSciNet review:
1653998
Fulltext PDF Free Access
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Abstract: Given an odd prime we show a way to construct large families of polynomials , , where is a set of primes of the form mod and is the irreducible polynomial of the Gaussian periods of degree in . Examples of these families when are worked in detail. We also show, given an integer and a prime mod , how to represent by matrices the Gaussian periods of degree in , and how to calculate in a simple way, with the help of a computer, irreducible polynomials for elements of .
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Additional Information
F. Thaine
Affiliation:
Department of Mathematics and Statistics  CICMA, Concordia University, 1455, de Maisonneuve Blvd. W., Montreal, Quebec, H3G 1M8, Canada
Email:
ftha@vax2.concordia.ca
DOI:
http://dx.doi.org/10.1090/S0025571899011424
PII:
S 00255718(99)011424
Received by editor(s):
May 19, 1998
Received by editor(s) in revised form:
October 15, 1998
Published electronically:
May 19, 1999
Additional Notes:
This work was supported in part by grants from NSERC and FCAR
Article copyright:
© Copyright 2000
American Mathematical Society
