Kowalski, E.; Michel, P.; VanderKam, J. Mollification of the fourth moment of automorphic \(L\)-functions and arithmetic applications. (English) Zbl 1054.11026 Invent. Math. 142, No. 1, 95-151 (2000). Summary: We compute the asymptotics of twisted fourth power moments of modular \(L\)-functions of large prime level near the critical line. This allows us to prove some new non-vanishing results on the central values of automorphic \(L\)-functions, in particular those obtained by base change from \(GL_2(\mathbb Q)\) to \(GL_2(K)\) for \(K\) a cyclic field of low degree. Cited in 6 ReviewsCited in 45 Documents MSC: 11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations 11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols 11M41 Other Dirichlet series and zeta functions × Cite Format Result Cite Review PDF Full Text: DOI Link