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The long gamma-ray burst (GRB) 100621A, at the time the brightest X-raytransient ever detected by Swift-XRT in the $0.3\textrm{--}10$ keV range, hasbeen observed with the H.E.S.S. imaging air Cherenkov telescope array,sensitive to gamma radiation in the very-high-energy (VHE, $>100$ GeV) regime.Due to its relatively small redshift of $z\sim0.5$, the favourable position inthe southern sky and the relatively short follow-up time ($<700 \rm{s}$ afterthe satellite trigger) of the H.E.S.S. observations, this GRB could be withinthe sensitivity reach of the H.E.S.S. instrument. The analysis of the H.E.S.S.data shows no indication of emission and yields an integral flux upper limitabove $\sim$380 GeV of $4.2\times10^{-12} \rm cm^{-2}s^{-1}$ (95 % confidencelevel), assuming a simple Band function extension model. A comparison to aspectral-temporal model, normalised to the prompt flux at sub-MeV energies,constraints the existence of a temporally extended and strong additional hardpower law, as has been observed in the other bright X-ray GRB 130427A. Acomparison between the H.E.S.S. upper limit and the contemporaneous energyoutput in X-rays constrains the ratio between the X-ray and VHE gamma-rayfluxes to be greater than 0.4. This value is an important quantity formodelling the afterglow and can constrain leptonic emission scenarios, whereleptons are responsible for the X-ray emission and might produce VHE gammarays.

Search for TeV Gamma-ray Emission from GRB 100621A, an extremely bright GRB in X-rays, with H.E.S.S