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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
Appendix A. Some Euler Products
This appendix is devoted to proving Lemma 8.3, 15.2, 15.3, 16.1 and 16.2. For notational simplicity we shall write
Proof of Lemma 8.3. Note that
which are henceforth assumed. We discuss in three cases.
Case 1. (q, dh) = 1.
We have
It follows that
This together with the relations
yields (A.1).
Case 2. q|h.
We have
so that
This yields (A.3).
This completes the proof.
Proof of Lemma 16.1. For any q, r, d and l we have
Hence
and
On the other hand we have
It follows that
It is direct to verify that in either case the assertion holds.
Proof of Lemma 16.2. We give a sketch only. If dl = 1 and |s − 1| ≤ 5α, then
with
The assertion follows by discussing the cases χ(2) 6= 1 and χ(2) = 1 respectively
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This paper is available on arxiv under CC 4.0 license.
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