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Author:
(1) Yitang Zhang.
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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
10. Proof of Proposition 2.4
The goal of this section is to prove Proposition 2.4. We continue to assume 1 ≤ j ≤ 3.
By Lemma 8.1 we have
The contour of integration is moved in the same way as the proof of Lemma 8.1. Thus, by Lemma 5.8 and 8.2,
This yields (10.8) since the function
Thus, with simple modification, Lemma 10.1 and 10.2 apply to the sums
Noting that
and gathering the above results together we conclude
with
Hence, by Proposition 7.1,
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This paper is available on arxiv under CC 4.0 license.
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