Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed

Authors:
Marko Moisio;Kalle Ranto
Affiliations:
Department of Mathematics and Statistics, University of Vaasa, PO Box 700, FIN-65101 Vaasa, Finland;Department of Mathematics, University of Turku, FIN-20014 Turku, Finland
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

Let F"q be a finite field of characteristic p=2,3. We give the number of irreducible polynomials x^m+a"m"-"1x^m^-^1+...+a"0@?F"q[x] with a"m"-"1 and a"m"-"3 prescribed for any given m if p=2, and with a"m"-"1 and a"1 prescribed for m=1,...,10 if p=2,3. In the latter case an enumeration formula, applicable also if m10, is given, but it is explicit only up to the evaluation of certain Kronecker class numbers.