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The pair correlation of zeros of the Riemann zeta function and distribution of primes

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Abstract.

Assuming a special version of the Montgomery-Odlyzko law on the pair correlation of zeros of the Riemann zeta function conjectured by Rudnick and Sarnak and assuming the Riemann Hypothesis, we prove new results on the prime number theorem, difference of consecutive primes, and the twin prime conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Shandong University, Jinan 250100, China, , , , , , CN

    J. Liu

  2. Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA, , , , , , US

    Y. Ye

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  1. J. Liu
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  2. Y. Ye
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Received: 4.6.1999

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Liu, J., Ye, Y. The pair correlation of zeros of the Riemann zeta function and distribution of primes. Arch. Math. 76, 41–50 (2001). https://doi.org/10.1007/s000130050540

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  • DOI: https://doi.org/10.1007/s000130050540

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