2018/09/26 by Gaál, István, Remete, László · 1 citation
#11R04 #11Y50 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1809.10072
Let m be an integer, m≠ -8,-3,0,5 such that m2+3m+9 is square free. Let α be a root of f=x6-2mx5-(5m+15)x4-20x3+5mx2+(2m+6)x+1. The totally real cyclic fields K=Q(α) are called simplest sextic fields and are well known in the literature. Using a completely new approach we explicitly give an integral basis of K in a parametric form and we show that the structure of this integral basis is periodic in m with period length 36. We prove that K is not monogenic except for a few values of m in which cases we give all generators of power integral bases.