A Remark on Density Theorems for Riemann’s Zeta-function: Proof of Theorem 1

Written by @escholar | Published on 2024/5/15

TL;DR —

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: pintz@renyi.hu

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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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