Understanding the Mean-Value Formula II with Primitive Characters
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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
14. Mean-value formula II
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Recall that we always assume ψ is a primitive character (mod p), p ∼ P. Sometimes we write pψ for the modulus p.
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Let k ∗ = {κ ∗ (m)} and a ∗ = {a ∗ (n)} denote sequences of complex numbers satisfying
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The goal of this section is to prove
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Proposition 14.1. Suppose |β| < 5α. Then
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This paper is available on arxiv under CC 4.0 license.
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