:::info
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
:::info
This paper is available on arxiv under CC 4.0 license.
:::