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

11 Nov 2019  ·  Goldston D. A., Turnage-Butterbaugh C. L. ·

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...

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Number Theory