Subconvex bounds for $U_{n+1}\times U_n$ in horizontal aspects

TL;DR

This paper proves subconvex bounds for L-functions associated with automorphic representations of unitary groups, specifically in horizontal aspects where ramified places vary, advancing understanding of their growth and bounds.

Contribution

It introduces new subconvex bounds for these L-functions in horizontal aspects, allowing the set of ramified places to vary, which was not previously established.

Findings

Established subconvex bounds in horizontal aspects

Allowed variation in ramified places

Enhanced understanding of automorphic L-functions

Abstract

For $L$-functions attached to automorphic representations of unitary groups $U_{n+1}\times U_n$, we establish a subconvex bound valid in certain horizontal aspects, where the set of ramified places is allowed to vary.