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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
18. Proof of Proposition 2.5
By the discussion at the end of Section 2, it suffices to prove (2.32) and (2.33).
Proof of (2.32).
By (12.3), (12,17), (13.7), (15.24), (16.17) and (17.10),
In view of (15.), we can write
By calculation (there is a theoretical interpretation),
Hence
Direct calculation shows that
It follows from (8.24), (9.8) and (18.2) that
This with together (8.23), (9.7) and (18.1) yields (2.32).
Proof of (2.33).
By Lemma 8.1,
We have
The right side is split into three sums according to
Thus we have the crude bound
so that
This yields (2.33) by Lemma 8.1 and Proposition 7.1
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This paper is available on arxiv under CC 4.0 license.
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