On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case

Abstract

We prove a Weyl-type subconvex bound for cube-free level Hecke characters over totally real number fields. Our proof relies on an explicit inversion to Motohashi's formula. Schwartz functions of various kinds and the invariance of the relevant Motohashi's distributions discovered in a previous paper play central roles.

References in corpus (8)

• The subconvexity problem for $\GL_{2}$
• The Weyl bound for Dirichlet $L$-functions of cube-free conductor
• Twisted L-functions over number fields and Hilbert's eleventh problem
• The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound
• Burgess-like subconvex bounds for $G{L}_2\times G{L}_1$
• Eisenstein series and the cubic moment for PGL(2)
• Deducing Selberg trace formula via Rankin-Selberg method for ${\mathrm{GL}}_2$
• Explicit Burgess-like subconvex bounds for ${\mathrm{GL}}_2\times {\mathrm{GL}}_1$