Subconvexity Problem on ${\mathrm{GL}}_3$ over number fields: the twist aspect

Abstract

Let $F$ denote a number field and let $\mathfrak{q}\subset O_F$ traverse a sequence of prime ideals with norm $N(\mathfrak{q})\to \infty$ and for each $\mathfrak{q}$, let $\chi \in \widehat{F^{\times }\setminus {\mathbb{A}}^{\times }}$ be a finite order character of conductor $\mathfrak{q}$. For a fixed unitary cuspidal automorphic representation $\pi$ of ${\mathrm{GL}}_3/F$ we show that \begin{equation*} L(π\otimes χ,\tfrac{1}{2})\ll \ N(\mathfrak{q})^{3/4-κ}.\end{equation*} holds for all $\kappa <\frac{1}{36}$.

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