JP Journal of Algebra, Number Theory and Applications
Volume 11, Issue 2, Pages 223 - 248
(August 2008)
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IRREDUCIBLE POLYNOMIALS WITH PRESCRIBED TRACE AND RESTRICTED NORM
K. Kononen (Finland), M. Moisio (Finland), M. Rinta-Aho (Finland) and K. V䤮䮥n (Finland)
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Abstract: Let
be a finite field with a primitive element
In this paper we use exponential sums and Jacobi sums to compute the number of the irreducible polynomials of degree m over
with trace fixed and norm restricted to a coset of a subgroup
We give the number explicitly for
and for
when
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Keywords and phrases: irreducible polynomials, monomial exponential sums, Gauss sums, Jacobi sums. |
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