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

Abstract

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