Small gaps and small spacings between zeta zeros
Volume 210 / 2023
Acta Arithmetica 210 (2023), 133-153
MSC: Primary 11M06; Secondary 11M26.
DOI: 10.4064/aa220731-15-2
Published online: 24 April 2023
Abstract
Assuming the Riemann hypothesis, we show that phenomena concerning pairs of zeros established via pair correlation methods occur (with at most a slight adjustment of the constants) with positive density. Also, while a multiple zero is commonly considered to generate a close pair of zeros, we introduce a new method that shows there are infinitely many gaps between distinct zeros that are smaller than the average spacing between zeros.
