A note on small gaps between zeros of the Riemann zeta-function

Assuming the Riemann Hypothesis, we improve on previous results by proving there are infinitely many zeros of the Riemann zeta-function whose differences are smaller than 0.50412 times the average spacing. To obtain this result, we generalize a set of weights that were developed by Xiaosheng Wu, who used them to find a positive proportion of large and small gaps between zeros of the Riemann zeta-function.
Comment: The authors have found a mistake in the preprint, which invalidates the calculations giving the result of Theorem 1. While the Wu weights are correct, the generalization only holds with functions (or polynomials) which are symmetric in all their variables. The authors do not yet know whether this restriction allows this method to improve on the earlier results or not; this is now work in progress.