Plus/minus p-adic L-functions for GL2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {GL}_{2n}$$\end{document}

We generalise Pollack’s construction of plus/minus L-functions to certain cuspidal automorphic representations of GL2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {GL_{2n}}$$\end{document} using the p-adic L-functions constructed in work of Barrera Salazar et al. (On p-adic l-functions for GL2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {GL}_{2n}$$\end{document} in finite slope shalika families, 2021). We use these to prove that the complex L-functions of such representations vanish at at most finitely many twists by characters of p-power conductor.