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Author:
(1) Yitang Zhang.
Appendix A. Some Euler products
Appendix B. Some arithmetic sums
In this section we establish an approximation to Ξ14.
Assume that ψ ∈ Ψ1 and ρ ∈ Z(ψ). By Lemma 5.2 and (2.2),
By Lemma 6.1,
and, by Lemma 5.1,
Hence
By Lemma 6.1 and 5.1,
We insert this into (13.2) and then insert the result into (13.1). Thus we obtain
where
where
Inserting this into (12.4) we obtain
Combining (2.34), Cauchy’s inequality, Proposition 7.1, Lemma 5.9, 6.1 and 3.3, we can verify that
For example, by (2.34)
the right side being estimated via Lemma 5.9, 6.1 and 3.3
This paper is available on arxiv under CC 4.0 license.