Abstract
An estimate on the Montgomery’s conjecture on the pair correlation of the zeros of the Riemann zeta function is given. An extension is given also to the zeros of Dirichlet L-functions.
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References
A. Connes, Trace formula on the adele class space and Weil positivity, Current developments in mathematics, 1997, International Press, 1999, 5–64.
A. Fujii, On the zeros of Dirichlet L-functions I, Trans. A. M. S. 196, (1974), 225–235.
A. Fujii, On the distribution of the zeros of the Riemann zeta function in short intervals, Proc. of Japan Academy 66, (1990), 75–79.
A. Fujii, On the gaps between the consecutive zeros of the Riemann zeta function, Proc. of Japan Academy 66, (1990), 97–100.
A. Fujii, Some observations concerning the distribution of the zeros of the zeta functions I, Advanced Studies in Pure Math. 21, (1992), 237–280.
A. Fujii, An additive theory of the zeros of the Riemann zeta function, Comment. Math. Univ. Sancti Pauli, 45, (1996), 49–116.
A. Fujii, Explicit formulas and oscillations, Emerging applications of number theory, IMA Vol. 109, Springer, 1999, 219–267.
A. Fujii and A. Ivic, On the distribution of the sums of the zeros of the Riemann zeta function, Comment. Math. Univ. Sancti Pauli, 49, (2000), 43–60.
N. Katz and P. Sarnak, Random matrices, Frobenius eigenvalues, and monodromy, AMS Colloq. Publ., Vol. 45, 1999.
H. L. Montgomery, The pair correlation of the zeros of the zeta function, Proc. Symp. Pure Math. 24, (1973), 181–193.
A. Selberg, Collected Works, Vol. I, 1989, Springer.
E. C. Titchmarsh, The theory of the Riemann zeta function (2nd ed. rev. by D. R. Heath-Brown), Oxford Univ. Press, 1951 (1988).
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Fujii, A. (2002). On the Pair Correlation of the Zeros of the Riemann Zeta Function. In: Jia, C., Matsumoto, K. (eds) Analytic Number Theory. Developments in Mathematics, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3621-2_8
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DOI: https://doi.org/10.1007/978-1-4757-3621-2_8
Publisher Name: Springer, Boston, MA
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