Special values of anticyclotomic \(L\)-functions.
The author extends his earlier results and methods [\textit{V. Vatsal}, Invent. Math. 148, No.~1, 1--46 (2002; Zbl 1119.11035)] on nonvanishing of \(L\)-functions associated to modular forms in the anticyclotomic tower of conductor \(p^\infty\) over an imaginary quadratic field to the case where the sign in the functional equation is \(-1\) (Theorem 1.4). In that case he shows, in particular, that derivatives of the \(L\)-functions are generically nonzero at the center. The main ingredient in the proof is a new ``Johnowitz congruence'' that relates the nontriviality of a special value modular curve. Applications are given to the Iwasawa \(\mu\)-invariant of the \(p\)-adic \(L\)-functions of Bartolini and Darmon (Theorem 1.1).
scientific article; zbMATH DE number 1911547
scientific article