Jacobi sums and new families of irreducible polynomials of Gaussian periods

Author:
F. Thaine

Journal:
Math. Comp. **70** (2001), 1617-1640

MSC (2000):
Primary 11R18, 11R21, 11T22

DOI:
https://doi.org/10.1090/S0025-5718-01-01312-6

Published electronically:
May 11, 2001

MathSciNet review:
1836923

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Let , an -th primitive root of 1, mod a prime number, a primitive root modulo and . We study the Jacobi sums , , where is the least nonnegative integer such that mod . We exhibit a set of properties that characterize these sums, some congruences they satisfy, and a MAPLE program to calculate them. Then we use those results to show how one can construct families , , of irreducible polynomials of Gaussian periods, , of degree , where is a suitable set of primes mod . We exhibit examples of such families for several small values of , and give a MAPLE program to construct more of them.

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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/S0025-5718-01-01312-6

Received by editor(s):
September 15, 1998

Received by editor(s) in revised form:
January 19, 2000

Published electronically:
May 11, 2001

Additional Notes:
This work was supported in part by grants from NSERC and FCAR

Article copyright:
© Copyright 2001
American Mathematical Society