The aim of this study is to search for evidence of a common emission engine between radio giant pulses (GPs) and very-high-energy (VHE, E>100 GeV) gamma-rays from the Crab pulsar. 16 hours of simultaneous observations of the Crab pulsar at 1.4 GHz with the Effelsberg radio telescope and the Westerbork Synthesis Radio Telescope (WSRT), and at energies above 60 GeV with the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes were performed. We searched for a statistical correlation between the radio and VHE gamma-ray emission with search windows of different lengths and different time lags to the arrival times of a radio GP. A dedicated search for an enhancement in the number of VHE gamma-rays correlated with the occurrence of radio GPs was carried out separately for the P1 and P2 phase ranges respectively. 99444 radio GPs have been detected in the radio data sample. We find no significant correlation between the GPs and VHE photons in any of the search windows. Depending on phase cuts and the chosen search windows we find upper limits at 95% confidence level on an increase in VHE gamma-ray events correlated with radio GPs between 7% and 61% of the average Crab pulsar VHE flux for the P1 and P2 phase ranges respectively. This puts upper limits on the flux increase during a radio GP of 12% to 2900% (depending on search window duration and phase cuts) of the pulsed VHE flux. This is the most stringent upper limit on a correlation between gamma-ray emission and radio GPs reported so far.}
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