Discrete Mean Estimates and the Landau-Siegel Zero: References
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Author:
(1) Yitang Zhang.
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Table of Links
Abstract & Introduction
Notation and outline of the proof
The set Ψ1
Zeros of L(s, ψ)L(s, χψ) in Ω
Some analytic lemmas
Approximate formula for L(s, ψ)
Mean value formula I
Evaluation of Ξ11
Evaluation of Ξ12
Proof of Proposition 2.4
Proof of Proposition 2.6
Evaluation of Ξ15
Approximation to Ξ14
Mean value formula II
Evaluation of Φ1
Evaluation of Φ2
Evaluation of Φ3
Proof of Proposition 2.5
Appendix A. Some Euler products
Appendix B. Some arithmetic sums
References
References
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[2] J. B. Conrey, A. Ghosh and S. M. Gonek, A note on gaps between zeros of the zeta function, Bull. London Math. Soc. 16(1984), 421-424.
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[3] J. B. Conrey, A. Ghosh and S. M. Gonek, Mean values of the Riemann zeta-function with application to the distribution of zeros, Number theory, trace formulas and discrete groups (Academic Press, Boston, 1989), 185-199.
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[4] J. B. Conrey, A. Ghosh and S. M. Gonek, Simple zeros of the Riemann zeta-function, Proc. London Math. Soc. (3)76(1998), 497-522.
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[7 ] H. Davenport, Multiplicative Number Theory, 3rd. ed. (revised by H. L. Montgomery), Springer-Verlag, New York, 2000
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[10] D. Goldfeld, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3(1976), 624-663.
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[13] D. R. Heath-Brown, Small class numbers and the pair correlation of zeros, Conference in Celebration of the Centenary of the the Proof of the Prime Number Theorem (A Symposium on the Riemann Hypothesis), Seattle, 1996.
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[17] H. L. Montgomery, The pair correlation of zeros of the zeta-function, Analytic number theory, Proc. Symp. Pure Math. Vol 24, 181-193, (Amer. Math. Soc., Providence, RI. 1973)
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This paper is available on arxiv under CC 4.0 license.
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