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

15 May 2024

This paper is available on arxiv under CC 4.0 license.


(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

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