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 the Large European Array for Pulsars .
The pulse energy distribution of GPs associated 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 are best-described by a broken power law , with the break occurring at \sim 7 Jy \SI { } { \micro \second } , 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 GP emission are measured , which are found to vary by \sim 0.5 at pulse phases close to the centre of the GP phase distributions .
We find the frequency-resolved structure of GPs to vary significantly , and in a manner that can not be attributed to the interstellar medium influence on the observed pulses .
We examine the distribution of polarisation fractions of the GPs and find no correlation between GP emission phase and fractional polarisation .
We use the GPs to time PSR B1937+21 and although the achievable time of arrival precision of the GPs is approximately a factor of two greater than that of the average pulse profile , there is a negligible difference in the precision of the overall timing solution when using the GPs .