Explicit Burgess-like subconvex bounds for ${\mathrm{GL}}_2\times {\mathrm{GL}}_1$

Abstract

We make the polynomial dependence on the fixed representation $\pi$ in our previous subconvex bound of $L(1/2,\pi \otimes \chi )$ for ${\mathrm{GL}}_2\times {\mathrm{GL}}_1$ explicit, especially with respect to the usual conductor $\mathbf{C}({\pi }_{\mathrm{fin}})$. There is no clue that the original choice, due to Michel & Venkatesh, 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.

References in corpus (2)

• Burgess-like subconvexity for ${\mathrm{GL}}_1$
• On sup-norm bounds part I: ramified Maaß newforms over number fields

Cited by in corpus (2)

• Explicit subconvexity for ${\mathrm{GL}}_2$
• On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case