Jacobi sums and new families of irreducible polynomials of Gaussian periods
Author:
F. Thaine
Journal:
Math. Comp. 70 (2001), 16171640
MSC (2000):
Primary 11R18, 11R21, 11T22
Published electronically:
May 11, 2001
MathSciNet review:
1836923
Fulltext PDF Free Access
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Abstract: 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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 F. Thaine, On the coefficients of Jacobi sums in prime cyclotomic fields, Trans. Amer. Math. Soc. 351 (1999), 47694790. MR 2000c:11181
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 A. Weil, Jacobi sums as ``Grössencharaktere'', Trans. Amer. Math. Soc. 73 (1952), 487495. MR 14d:452d
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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/S0025571801013126
PII:
S 00255718(01)013126
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
