Numerical Calculation of Ξ12: Detailed Analysis and Findings

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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

References

9. Evaluation of Ξ12


Thus, in a way similar to the proof of (8.12), we deduce that


where


It follows by Proposition 7.1 that


This yields


where


with


Numerical calculation shows that


It follows that

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This paper is available on arxiv under CC 4.0 license.

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