Explore the detailed evaluation of Φ1, incorporating key lemmas, propositions, and advanced mathematical techniques for comprehensive understanding.
Author: Yitang Zhang. Table of Links Abstract & Introduction Notation and outline of the proof The set Ψ1 Zeros of LL in Ω Some analytic lemmas Approximate formula for L 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 15.
1 we obtain This yields, by , To apply we need two lemmas which will be proved in Appendix A. Lemma 15.2. If |s − 1| 1 we have b On the other hand, we can write with It follows by - and Proposition 14.1 that where The innermost sum above is, by the Mellin transform, equal to where This yields Hence where On substituting n=mk we can writ n=mk with Hence it follows that If =1, then q, dl so that for σ > 9/10.
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