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We 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.

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