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

TL;DR

This paper establishes a subconvexity bound for twisted L-functions of automorphic representations on GL(3) over number fields, improving the known bounds in the twist aspect as the conductor grows.

Contribution

It proves a new subconvexity bound for GL(3) L-functions twisted by characters of increasing conductor over number fields, advancing the understanding of their growth.

Findings

Established a subconvexity bound with exponent 3/4 - 1/36 for GL(3) L-functions.

Extended subconvexity results to the twist aspect over general number fields.

Demonstrated the bound holds uniformly for characters with conductor tending to infinity.

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 $\operatorname{GL}_3/F$ we show that \begin{equation*} L(\pi \otimes \chi,\tfrac{1}{2})\ll \ N(\mathfrak{q})^{3/4-\kappa}.\end{equation*} holds for all $\kappa< \frac{1}{36}$.