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We have studied 4265 giant pulses (GPs) from the millisecond pulsar B1937+21;the largest-ever sample gathered for this pulsar, in observations made with theLarge European Array for Pulsars. The pulse energy distribution of GPsassociated with the interpulse are well-described by a power law, with index$\alpha = -3.99 \pm 0.04$, while those associated with the main pulse arebest-described by a broken power law, with the break occurring at $\sim7$ Jy$\mu$s, with power law indices $\alpha_{\text{low}} = -3.48 \pm 0.04$ and$\alpha_{\text{high}} = -2.10 \pm 0.09$. The modulation indices of the GPemission are measured, which are found to vary by $\sim0.5$ at pulse phasesclose to the centre of the GP phase distributions. We find thefrequency-resolved structure of GPs to vary significantly, and in a manner thatcannot be attributed to the interstellar medium influence on the observedpulses. We examine the distribution of polarisation fractions of the GPs andfind no correlation between GP emission phase and fractional polarisation. Weuse the GPs to time PSR B1937+21 and although the achievable time of arrivalprecision of the GPs is approximately a factor of two greater than that of theaverage pulse profile, there is a negligible difference in the precision of theoverall timing solution when using the GPs.

A detailed study of giant pulses from PSR B1937+21 using the Large European Array for Pulsars