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



Importance of large gaps between zeros of zeta function?
Here are two papers that show a connection between the spacing of the zeros of the zeta function and the class number problem for imaginary quadratic fields:


Conrey, J. B., and H. Iwaniec, “Spacing of zeros of Hecke L-functions and the
class number problem.”


Montgomery, H. L., and P. J. Weinberger, “Notes on small class numbers.”


And of course the study of the pair correlation of the ordinates of the zeros of the zeta-function inspired the connection between the zeta function and random matrix theory. I believe some results about the gaps are ways to check that the zeros are spaced according to predictions that come from random matrix theory.


