Sign changes in short intervals related to Rankin-Selberg L-functions in the level aspect

In this paper, we investigate the sign-change problem for Fourier coefficients of two and three newforms. One of our main ingredients is determine the Rankin-Selberg L-functions corresponding to the configurations GL4xGL4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {GL}_4\times \text {GL}_4$$\end{document} and GL8xGL8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {GL}_8\times \text {GL}_8$$\end{document} in the level aspect concluding the local factors at ramified and unramified places, as well as the first or second moment related to these L-functions in the level aspect. We improve and generalize previous results.