Discrete Mean Estimates and the Landau-Siegel Zero: Proof of Proposition 2.6

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The proof of Proposition 2.6 leverages results from Section 9 and Cauchy’s inequality to simplify and demonstrate the proposition.

Table of Links

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

References

11. Proof of Proposition 2.6

By the result of Section 9,

Hence, by Cauchy’s inequality, the proof of Proposition 2.6 is reduced to showing that