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 L -functions attached to a cuspidal automorphic representation of G L m / Q GL_m/Q . For this, we apply the higher-level correlation asymptotic of Hejhal, Rudnick, and Sarnak in conjunction with semidefinite programming bounds.