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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
16. Evaluation of Φ2
Recall that Φ2 is given by (13.9). Write
Similar to (15.3),
where
The following lemma will be proved in Appendix A.
Lemma 16.2. The function
is analytic and bounded for σ > 9/10. Further we have
The contour of integration is moved in the same way as in the proof of Lemma 8.4. Thus the right side above is, by Lemma 16.2, equal to
Hence, by (16.15),
Inserting this into (16.13) and applying Lemma 16.1 we obtain
On the other hand, by Lemma 5.8 and direct calculation,
so that
This together with (16.16) and (16.12) yields
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This paper is available on arxiv under CC 4.0 license.
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