Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# Deriving Von Koch's Inequality Without Using the Riemann Hypothesis

Version 1 : Received: 25 November 2021 / Approved: 6 December 2021 / Online: 6 December 2021 (12:57:54 CET)
Version 2 : Received: 6 May 2022 / Approved: 6 May 2022 / Online: 6 May 2022 (12:45:00 CEST)

How to cite: Fujino, S. Deriving Von Koch's Inequality Without Using the Riemann Hypothesis. Preprints 2021, 2021120074 (doi: 10.20944/preprints202112.0074.v2). Fujino, S. Deriving Von Koch's Inequality Without Using the Riemann Hypothesis. Preprints 2021, 2021120074 (doi: 10.20944/preprints202112.0074.v2).

## Abstract

In this paper, we derive Von Koch's inequality without using the Riemann Hypothesis. As well known, Von Koch's inequality is equivalent to the Riemann Hypothesis. Namely, we show that the Riemann Hypothesis is true. Furthermore, we show that the upper limit of its can be lowered.

## Keywords

Number theory; Von Koch's inequality; Riemann Hypothesis

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comment 1
Commenter: Seiji Fujino
Commenter's Conflict of Interests: Author
Comment: The following has been corrected.
1. Fixed Abstract, Conclusion and Acknowledge.
2. Corrected unclear part of description (unified the meaning of $\alpha$ to Constant, etc.)
3. Corrected references.
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