On the trace formula of the Hecke operators and the special values of the second L-functions attached to the Hilbert modular forms
In [Modular Funct. of one Var. VI, Lect. Notes Math. 627, 105-169 (1977; Zbl 0372.10017)] \textit{D. Zagier} constructed modular forms for Sl(2, \({\mathbb{Z}})\) with the remarkable property that the Petersson scalar product of these forms with any eigenform f of the Hecke algebra is essentially given by a value of the ''second L-function'' attached to f. Among other things one can get from this construction the Eichler-Selberg trace formula for the action of Hecke operators on the space of cusp forms. In the paper under review the author shows that Zagier's method also works for Hilbert modular forms for totally real number fields with narrow class number one.
scientific article; zbMATH DE number 3970838
scientific article