Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions III: The Twisted Case

Abstract

This is a sequel to our previous articles \cite{Kw23, Kw23a+}. In this work, we apply recent techniques that fall under the banner of `Period Reciprocity' to study moments of $GL(3)\times GL(2)$ $L$-functions in the non-archimedean aspects, with a view towards the `Twisted Moment Conjectures' formulated by CFKRS.