Multiplicity of nontrivial zeros of primitive L-functions via higher-level correlations

We give universal bounds on the fraction of nontrivial zeros having given multiplicity for L-functions attached to a cuspidal automorphic representation of ${\mathrm{G}\mathrm{L}}_m\mathrm{/}\mathbb{Q}$. For this, we apply the higher-level correlation asymptotic of Hejhal and Rudnick & Sarnak in conjunction with semidefinite programming bounds.