ON SPLITTING OF PRIMES IN CUBIC NUMBER FIELDS WITH CLASS NUMBER 3

We show that splitting of primes in a cubic number field with class number 3 is homogenous if and only if the degree of the splitting field of its Hilbert class field is ⩽2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\leqslant 2$$\end{document}.