Geodesic
Hilbert cusp forms and special values of Dirichlet series of Rankin type
Glasgow mathematical journal, Tome 40 (1998) no. 1, pp. 71-77

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

Let K be a totally real number field of degree nover Q and let c be an integral ideal of a maximal order of K. Given a nonnegative integer j and a Hecke character on the group of ideles of K, let denote the space of Hilbert cusp forms of holomorphic type on Hn of weight j, level c and character ψ where Hn is the n-th power of the Poincaré upper half plane H.Let g be an element of , where 1 is the trivial character. If u ∈ Sk(c, ψ), then the product gu is an element of Sk+l (c, ψ), and therefore we can consider the linear map sending u to gu. Let be the adjoint of the linear map Φg with respect to the Petersson inner product. 
Lee, Min Ho. Hilbert cusp forms and special values of Dirichlet series of Rankin type. Glasgow mathematical journal, Tome 40 (1998) no. 1, pp. 71-77. doi: 10.1017/S0017089500032365
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