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Hilbert cusp forms and special values of Dirichlet series of Rankin type
Published online by Cambridge University Press: 18 May 2009
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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.
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- Copyright © Glasgow Mathematical Journal Trust 1998