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Small gaps and small spacings between zeta zeros

Volume 210 / 2023

Hung M. Bui, Daniel A. Goldston, Micah B. Milinovich, Hugh L. Montgomery Acta Arithmetica 210 (2023), 133-153 MSC: Primary 11M06; Secondary 11M26. DOI: 10.4064/aa220731-15-2 Published online: 24 April 2023


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.


  • Hung M. BuiDepartment of Mathematics
    University of Manchester
    Manchester M13 9PL, UK
  • Daniel A. GoldstonDepartment of Mathematics and Statistics
    San Jose State University
    San Jose, CA 95192, USA
  • Micah B. MilinovichDepartment of Mathematics
    University of Mississippi
    University, MS 38677, USA
  • Hugh L. MontgomeryDepartment of Mathematics
    University of Michigan
    Ann Arbor, MI 48109, USA

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