Explicit Burgess-like subconvex bounds for \(\mathrm{GL_2 \times GL_1}\). (English) Zbl 1469.11127
Summary: We make the polynomial dependence on the fixed representation \(\pi\) in our previous subconvex bound of \(L(\frac{1}{2}, \pi \otimes \chi)\) for \(\mathrm{GL_2 \times GL}_1\) explicit, especially in terms of the usual conductor \(\mathbf{C}(\pi_{\text{fin}})\). There is no clue that the original choice, due to P. Michel and A. Venkatesh [Publ. Math., Inst. Hautes Étud. Sci. 111, 171–271 (2010; Zbl 1376.11040)], of the test function at the infinite places should be the optimal one. Hence we also investigate a possible variant of such local choices in some special situations.
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 |
Citations:
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