A twisted adjoint \(L\)-value of an elliptic modular form
Let \(f\) be a primitive elliptic cusp form and let \(\chi\) be a quadratic character. Consider the twisted adjoint \(L\)-function \(L(s, \text{Ad}(f)\otimes \chi)\) for \(f\) and \(\chi\). It has been conjectured that the special value of \(L(s, \text{Ad}(f)\otimes \chi)\) at \(s=1\) is closely related to the discriminant of Hecke fields by \textit{K. Doi, H. Hida} and \textit{H. Ishii} [Invent. Math. 134, 547-577 (1998; Zbl 0924.11035 above)]. The author of this paper calculates the numerical examples of the calculations of special values of the twisted adjoint \(L\)-function \(L(s, \text{Ad}(f) \otimes\chi)\) and proves that they support the conjecture.
scientific article; zbMATH DE number 1268043