I have noticed that there are quite a few publications, many of them recent, on trying to determine the supremum of the gaps (normalized) between zeros of $\zeta \left(\frac{1}{2} + i t \right)$. Several make use of Wirtinger's inequality. I've been studying some of these papers in an attempt to broaden my knowledge of the zeta function.

My question is this - why are people interested in determining information about the gaps? I assume that there must be some information encoded in the gap sizes about the distribution of prime numbers. Is there a publication or book in which I could read about the reasons for studying the gaps?

Thanks, Tom