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We give universal bounds on the fraction of nontrivial zeros having givenmultiplicity for L-functions attached to a cuspidal automorphic representationof $\mathrm{GL}_m/\mathbb{Q}$. For this, we apply the higher-level correlationasymptotic of Hejhal and Rudnick & Sarnak in conjunction with semidefiniteprogramming bounds.

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