Understanding the Mean-Value Formula II with Primitive Charactersby@eigenvalue

# Understanding the Mean-Value Formula II with Primitive Characters

June 2nd, 2024

## Too Long; Didn't Read

Mean-Value Formula II involves proving Proposition 14.1, using primitive characters and sequences of complex numbers to establish the result under the condition |β| < 5α.

Author:

(1) Yitang Zhang.

Appendix A. Some Euler products

Appendix B. Some arithmetic sums

References

## 14. Mean-value formula II

Recall that we always assume ψ is a primitive character (mod p), p ∼ P. Sometimes we write pψ for the modulus p.

Let k ∗ = {κ ∗ (m)} and a ∗ = {a ∗ (n)} denote sequences of complex numbers satisfying

The goal of this section is to prove

Proposition 14.1. Suppose |β| < 5α. Then

This paper is available on arxiv under CC 4.0 license.

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