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On the distribution of imaginary parts of zeros of the Riemann zeta function, II

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Abstract

We continue our investigation of the distribution of the fractional parts of αγ, where α is a fixed non-zero real number and γ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. We establish some connections to Montgomery’s pair correlation function and the distribution of primes in short intervals. We also discuss analogous results for a more general L-function.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL, 61801, USA

    Kevin Ford & Alexandru Zaharescu

  2. Department of Mathematics, Stanford University, 450 Serra Mall, Bldg. 380, Stanford, CA, 94305, USA

    K. Soundararajan

Authors
  1. Kevin Ford
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  2. K. Soundararajan
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  3. Alexandru Zaharescu
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Corresponding author

Correspondence to Kevin Ford.

Additional information

The first author is supported by National Science Foundation Grant DMS-0555367. The second author is partially supported by the National Science Foundation and the American Institute of Mathematics (AIM). The third author is supported by National Science Foundation Grant DMS-0456615.

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Ford, K., Soundararajan, K. & Zaharescu, A. On the distribution of imaginary parts of zeros of the Riemann zeta function, II. Math. Ann. 343, 487–505 (2009). https://doi.org/10.1007/s00208-008-0280-x

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  • DOI: https://doi.org/10.1007/s00208-008-0280-x

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