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
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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