Discover the essential analytic lemmas and their proofs crucial for understanding Dirichlet L-functions, including the Deuring-Heilbronn phenomenon.
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 5.
As a consequence of Lemma 5.3, the Mellin transform is analytic for σ > 0. Lemma 5.4 . . If 1/2 ≤ σ ≤ 2, then Lemma 5.4 If 1/2 ≤ σ ≤ 2, then . If |s − 1| < 10α, then then Proof . . Using partial integration twice we obtain Proof By we have Thus some upper bounds for ∆′′ analogous to Lemma 5.3 can be obtained, and follows. Throughout the rest of this paper we assume that holds. This assumption will not be repeated in the statements of the lemmas and propositions in the sequel.
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