On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function
Journal of Mathematical Analysis and Applications(2023)
Abstract
Assuming the Riemann Hypothesis, it is known that there are infinitely many consecutive pairs of zeros of the Riemann zeta-function within 0.515396 times the average spacing. This is obtained using the method of Montgomery and Odlyzko. We prove that this method can never find infinitely many pairs of consecutive zeros within 0.5042 times the average spacing.
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Key words
montgomery–odlyzko method,zeros,zeta-function
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