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We report on a search for ultra-high-energy (UHE) neutrinos from gamma-raybursts (GRBs) in the data set collected by the Testbed station of the AskaryanRadio Array (ARA) in 2011 and 2012. From 57 selected GRBs, we observed noevents that survive our cuts, which is consistent with 0.12 expected backgroundevents. Using NeuCosmA as a numerical GRB reference emission model, we estimateupper limits on the prompt UHE GRB neutrino fluence and quasi-diffuse flux from$10^{7}$ to $10^{10}$ GeV. This is the first limit on the prompt UHE GRBneutrino quasi-diffuse flux above $10^{7}$ GeV.

Constraints on the Ultra-High Energy Neutrino Flux from Gamma-Ray Bursts from a Prototype Station of the Askaryan Radio Array