Rapid computation of \(L\)-functions for modular forms. (English) Zbl 1381.11046
Summary: Let \(f\) be a fixed (holomorphic or Maass) modular cusp form, with an \(L\)-function \(L(f,s)\). We describe an algorithm that computes the value \(F(f,\frac{1}{2} +iT)\) to any specified precision in time \(O(1+| T |^{7/8})\).
MSC:
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11F66 | Langlands \(L\)-functions; one variable Dirichlet series and functional equations |
| 11Y35 | Analytic computations |
