New criteria for canonical number systems

Shigeki Akiyama, Hui Rao
2004 Acta Arithmetica  
Let P (x) = x d + p d−1 x d−1 + · · · + p 0 be an expanding monic polynomial with integer coefficients. If each element of Z[x]/P (x)Z[x] has a polynomial representative with coefficients in [0, |p 0 | − 1] then P (x) is called a canonical number system generating polynomial, or a CNS polynomial in short. A method due to Hollander [6] is employed to study CNS polynomials. Several new criteria for canonical number system generating polynomials are given and a conjecture of S.Akiyama & A.Pethő
more » ... kiyama & A.Pethő [3] is proved. The known results, especially an algorithm of H. Brunotte's in [4] and a recent work of K. Scheicher & J.M.Thuswaldner [15], can be derived by this new method in a simpler way. 1991 Mathematics Subject Classification. 11A63, 37B10.
doi:10.4064/aa111-1-2 fatcat:texzb43r7naxzgbozg3dn3mdbe