**Author:**

(1) Yitang Zhang.

## Table of Links

- Abstract & Introduction
- Notation and outline of the proof
- The set Î¨1
- Zeros of L(s, Ïˆ)L(s, Ï‡Ïˆ) in â„¦
- Some analytic lemmas
- Approximate formula for L(s, Ïˆ)
- Mean value formula I
- Evaluation of Îž11
- Evaluation of Îž12
- Proof of Proposition 2.4
- Proof of Proposition 2.6
- Evaluation of Îž15
- Approximation to Îž14
- Mean value formula II
- Evaluation of Î¦1
- Evaluation of Î¦2
- Evaluation of Î¦3
- Proof of Proposition 2.5

Appendix A. Some Euler products

Appendix B. Some arithmetic sums

## 11. Proof of Proposition 2.6

By the result of Section 9,

Hence, by Cauchyâ€™s inequality, the proof of Proposition 2.6 is reduced to showing that

This paper is available on arxiv under CC 4.0 license.