Author:
(1) Yitang Zhang.
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
13. Approximation to Ξ14
In this section we establish an approximation to Ξ14.
Assume that ψ ∈ Ψ1 and ρ ∈ Z(ψ). By Lemma 5.2 and (2.2),
By Lemma 6.1,
and, by Lemma 5.1,
Hence
By Lemma 6.1 and 5.1,
We insert this into (13.2) and then insert the result into (13.1). Thus we obtain
where
where
Inserting this into (12.4) we obtain
Combining (2.34), Cauchy’s inequality, Proposition 7.1, Lemma 5.9, 6.1 and 3.3, we can verify that
For example, by (2.34)
the right side being estimated via Lemma 5.9, 6.1 and 3.3
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