Families of irreducible polynomials

of Gaussian periods and matrices

of cyclotomic numbers

Author:
F. Thaine

Journal:
Math. Comp. **69** (2000), 1653-1666

MSC (1991):
Primary 11R18, 11R21, 11T22

DOI:
https://doi.org/10.1090/S0025-5718-99-01142-4

Published electronically:
May 19, 1999

MathSciNet review:
1653998

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-99-01142-4

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