skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Goldston, Daniel Alan"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; ; (, Acta Arithmetica)
    Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assuming RH, at least 67.9% of the nontrivial zeros are simple. Here we obtain an unconditional form of Montgomery’s theorem and show how to apply it to prove the following result on simple zeros: If all the zeros ρ=β+iγ of the Riemann zeta-function such that T3/8<γ≤T satisfy ∣∣β−1/2∣∣<1/(2logT), then, as T tends to infinity, at least 61.7% of these zeros are simple. The method of proof neither requires nor provides any information on whether any of these zeros are or are not on the critical line where β=1/2. We also obtain the same result under the weaker assumption of a strong zero-density hypothesis. 
    more » « less
    Full Text Available