Plus/minus p-adic L-functions for mathrm {GL}_{2n}

Abstract

We generalise Pollack’s construction of plus/minus L-functions to certain cuspidal automorphic representations of mathrm {GL_{2n}} using the p-adic L-functions constructed in work of Barrera Salazar et al. (On p-adic l-functions for text {GL}_{2n} 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.