A remark on the normalization of the standard zeta values for Siegel modular forms
This note is on the relationship of special values of the standard L-function and congruence of Siegel modular forms. The main result is an improvement of previous results given in [Math. Z. 259, No. 1, 97--111 (2008; Zbl 1173.11029)]. The crucial ingredient is Lemma \(4.2\), a construction of a value \(I\) from a finite dimensional Hermitian vector space \(V\) with given orthogonal basis and two functionals. The values turns out to be independent on the choice of the basis. Finally this type of normalization is applied on the topic of special values, such that the value only depends on the underlying eigenvalue system of the involved cuspidal Hecke eigenform. This leads to Theorem 4.3 which improves the results from the previous paper from above.
scientific article; zbMATH DE number 5723788