On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function

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.

arXiv comment6 pages, V2 contains changes to the exposition, clarification of the evaluation of S_1 on page 2, and corrections made to the choice of constants at the end of the proof