A Remark on Density Theorems for Riemann’s Zeta-function: Proof of Theorem 1
by EScholar: Electronic Academic Papers for ScholarsMay 15th, 2024
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A remark on density theorems for Riemann’s Zeta-function.
This paper is available on arxiv under CC 4.0 license.
Authors:
(1) J´anos Pintz, Supported by the National Research Development and Innovation Office, NKFIH, KKP 133819, ELKH Alfr´ed R´enyi Mathematical Institute H-1053 Budapest Realtanoda u. 13–15. Hungary and e-mail: [email protected]
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3 Proof of Theorem 1
Remark. If N ≥ T then the simple Theorem 4.11 of [Tit1951] (provable by simple partial summation) yields
Similarly to (4.2) of [Pin2023] we start with
Summarizing the above we get
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