Geodesic
The transition constant for arithmetic hyperbolic reflection groups
Izvestiya. Mathematics, Tome 75 (2011) no. 5, pp. 971-1005

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Using the results and methods of our papers [1], [2], we show that the degree of the ground field of an arithmetic hyperbolic reflection group does not exceed 25 in dimensions $n\geqslant 6$, and 44 in dimensions 3, 4, 5. This significantly improves our estimates obtained in [2]–[4]. We also use recent results in [5] and [6] to reduce the last bound to 35. We also review and correct the results of [1], § 1.
Keywords: group generated by reflections, arithmetic group, hyperbolic space, number field, field of definition, quadratic form. 
V. V. Nikulin. The transition constant for arithmetic hyperbolic reflection groups. Izvestiya. Mathematics, Tome 75 (2011) no. 5, pp. 971-1005. http://geodesic.mathdoc.fr/item/IM2_2011_75_5_a5/
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