Hybrid bounds for ${\rm{GL}}(4)\times {\rm{GL}}(1)$ twisted $L$-functions

TL;DR

This paper establishes a hybrid subconvexity bound for twisted L-functions on GL(4) in both level and conductor aspects, advancing understanding of their behavior in specific prime ranges.

Contribution

It provides the first hybrid subconvexity bound for GL(4) × GL(1) L-functions in the specified prime range, combining level and conductor aspects.

Findings

Proves a hybrid subconvexity bound for GL(4) × GL(1) L-functions.

Establishes bounds valid when M^{1/5}<P<M^{2/5}.

Advances the understanding of L-function behavior in hybrid aspects.

Abstract

Let $P,M$ be a two primes such that $(P,M)=1$. Let $\Pi$ be a normalized Hecke-Maa\ss\ form on ${\rm{GL}}(4)$ of level $P$, and $\chi$ a primitive Dirichlet character modulo $M$. In this paper, we study the hybrid subconvexity problem for $L(s, \Pi\otimes \chi)$ simultaneously in the level and conductor aspects. Among other things, we prove a hybrid subconvex bound, so long as $M^{1/5}<P<M^{2/5}$.