Geodesic
Automorphy factors for a Hilbert modular group
Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 231-236

Voir la notice de l'article provenant de la source Cambridge University Press

Let K be a totally real algebraic number field of degree n > 1, and let OK be the maximal order. We denote by гk, the Hilbert modular group SL2(OK) associated with K. On the extent of the weight of an automorphy factor for гK, some restrictions are imposed, not as in the elliptic modular case. Maass [5] showed that the weight is integral for K = Q(√5). It was shown by Christian [1] that for any Hilbert modular group it is a rational number with the bounded denominator depending on the group. 
Tsuyumine, Shigeaki. Automorphy factors for a Hilbert modular group. Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 231-236. doi: 10.1017/S0017089500007278
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