Discrete Mean Estimates and the Landau-Siegel Zero: Referencesby@eigenvalue

Discrete Mean Estimates and the Landau-Siegel Zero: References

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Yitang Zhang's paper delves into advanced topics in number theory, including proofs of propositions, analysis of Euler products, arithmetic sums, and mean value formulas, supported by references to seminal works in the field.
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(1) Yitang Zhang.

  1. Abstract & Introduction
  2. Notation and outline of the proof
  3. The set Ψ1
  4. Zeros of L(s, ψ)L(s, χψ) in Ω
  5. Some analytic lemmas
  6. Approximate formula for L(s, ψ)
  7. Mean value formula I
  8. Evaluation of Ξ11
  9. Evaluation of Ξ12
  10. Proof of Proposition 2.4
  11. Proof of Proposition 2.6
  12. Evaluation of Ξ15
  13. Approximation to Ξ14
  14. Mean value formula II
  15. Evaluation of Φ1
  16. Evaluation of Φ2
  17. Evaluation of Φ3
  18. Proof of Proposition 2.5

Appendix A. Some Euler products

Appendix B. Some arithmetic sums



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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.

[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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[7 ] H. Davenport, Multiplicative Number Theory, 3rd. ed. (revised by H. L. Montgomery), Springer-Verlag, New York, 2000

[8] D. Goldfeld, A simple proof of Siegel’s theorem, Proc. Nat. Acad. Sci. USA 71(1974), 1055.

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[11] A. Granville and H. M. Stark, ABC implies no “Siegel zeros” for L-functions of characters with negative discriminant, Invent. Math. 139(2000), 509-523.

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[15] H. Iwaniec and P. Sarnak, The non-vanishing of central values of automorphic Lfunctions and Landau-Siegel zeros, Israel J. Math., 120(2000), 155-177.

[16] A. Karatsuba, Basic Analytic Number Theory, (translated from Russian by M. Nathanson), Springer-Verlag, New York, 1993.

[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)

[18] C. L. Siegel, Uber die Classenzahl quadratischer Zuhlk¨orper, ¨ Acta Arith. 1(1936), 83-86.

[19] E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd. ed. (revised by D. R. Heath-Brown), Oxford Univ. Press, Oxford, 1986

This paper is available on arxiv under CC 4.0 license.