On Ground Fields of Arithmetic Hyperbolic Reflection Groups. II

This paper continues two our papers that appeared in 2007. Using our methods of 1980, 1981, some explicit finite sets of number fields containing all ground fields of arithmetic hyperbolic reflection groups in dimensions at least 4 are defined, and good explicit bounds of their degrees (over $\mathbb Q$) are obtained. This extends the results of our previous paper where it was done in dimensions at least 6. These results could be important for the further classification of these groups.