 
Summary: 1
1
Cubic CNS polynomials,
notes on a conjecture of W.J. Gilbert
Shigeki Akiyama y
Department of Mathematics, Faculty of Science,
Niigata University, Ikarashi 28050, Niigata 9502181, Japan,
Horst Brunotte
HausEndtStr. 88, D  40593 Dusseldorf, Germany
and
Attila Peth}o z
Institute of Mathematics and Computer Science, University of Debrecen,
P.O. Box 12, H  4010 Debrecen, Hungary
October 14, 2002
Abstract
A conjecture of W. J. Gilbert's on canonical number systems which are dened by cubic
polynomials is partially proved, and it is shown that the conjecture is not complete. Appli
cations to power integral bases of simplest and pure cubic number elds are given thereby
extending results of S. Kormendi.
