An explicit Watson-Ichino formula with CM newforms

TL;DR

This paper develops an explicit Watson-Ichino formula for specific L-functions involving a Hecke--Maass form and a CM newform, advancing the understanding of their special values.

Contribution

It extends previous work to provide an explicit formula for L(1/2,f⊗ad g) where f is a Hecke--Maass form and g is a CM newform, filling a gap in the literature.

Findings

Derived an explicit Watson-Ichino formula for the specified L-value.

Applied the formula to analyze the behavior of these L-functions.

Enhanced the toolkit for studying automorphic forms and their L-values.

Abstract

In this paper, we extend the work of Humphries and Khan [HK20] to establish an explicit version of Watson--Ichino formula for $L(1/2,f\otimes\mathrm{ad} g)$, where $f$ is a Hecke--Maass form and $g$ is a CM newform.