Spectral moment formulae for \(GL(3)\times GL(2)\) L-functions III: the twisted case

This is a sequel to our previous articles (Kwan in Algebra Number Theory. arXiv:2112.08568v4; Kwan in Spectral moment formulae for \(GL(3)\times GL(2)\) $GL(3)\times GL(2)$ L-functions II: Eisenstein case, 2023. arXiv:2310.09419). In this work, we apply recent techniques that fall under the banner of ‘Period Reciprocity’ to study moments of \(GL(3)\times GL(2)\) $GL(3)\times GL(2)$ L-functions in the non-archimedean aspects, with a view towards the ‘Twisted Moment Conjectures’ formulated by CFKRS.