A uniform Weyl bound for L-functions of Hilbert modular forms

Abstract

We establish a Weyl-type subconvexity of $L(\frac{1}{2},f)$ for spherical Hilbert newforms $f$ with level ideal ${\mathfrak{N}}^2$, in which $\mathfrak{N}$ is required to be cube-free, and at any prime ideal $\mathfrak{p}$ with ${\mathfrak{p}}^2\mid \mathfrak{N}$ the local representation generated by $f$ is not supercuspidal. The proof exploits a distributional version of Motohashi's formula over number fields developed by the first author, as well as Katz's work on hypergeometric sums over finite fields in the language of $\ell$-adic cohomology.

A mistake in the earlier version on the quality of the result is corrected