Subconvexity for $L$-Functions on $\mathrm{GL}_3$ over Number Fields

TL;DR

This paper establishes subconvexity bounds for certain $ ext{GL}_3$ $L$-functions over number fields, advancing understanding of their growth and distribution in specific aspects.

Contribution

It proves subconvexity bounds for self-dual $ ext{GL}_3$ $L$-functions in the $t$-aspect and for $ ext{GL}_3 imes ext{GL}_2$ $L$-functions in the $ ext{GL}_2$ Archimedean aspect over arbitrary number fields.

Findings

Established subconvexity bounds in the $t$-aspect for $ ext{GL}_3$ $L$-functions.

Proved subconvexity bounds in the $ ext{GL}_2$ Archimedean aspect for $ ext{GL}_3 imes ext{GL}_2$ $L$-functions.

Extended subconvexity results to arbitrary number fields.

Abstract

In this paper, over an arbitrary number field, we prove subconvexity bounds for self-dual $\mathrm{GL}_3$ $L$-functions in the $t$-aspect and for self-dual $\mathrm{GL}_3 \times \mathrm{GL}_2$ $L$-functions in the $\mathrm{GL}_2$ Archimedean aspect.