On the zeros of the Riemann zeta function

TL;DR

The paper discusses the author's previous failed attempt to prove the Riemann Hypothesis, identifies the error in that proof, and presents a new, seemingly correct proof of the hypothesis, along with reflections on the review process.

Contribution

It introduces a new proof of the Riemann Hypothesis and highlights issues in the mathematical review process.

Findings

Previous proof contained an error in connecting lemmas.

New proof appears correct so far.

Raises concerns about the review process in mathematics.

Abstract

In 2008 I thought I found a proof of the Riemann Hypothesis, but there was an error. In the Spring 2020 I believed to have fixed the error, but it cannot be fixed. I describe here where the error was. It took me several days to find the error in a careful checking before a possible submission to a payable review offered by one leading journal. There were three simple lemmas and one simple theorem, all were correct, yet there was an error: what Lemma 2 proved was not exactly what Lemma 3 needed. So, it was the connection of the lemmas. This paper came out empty, but I have found a different proof of the Riemann Hypothesis and it seems so far correct. In the discussion at the end of this paper I raise a matter that I think is of importance to the review process in mathematics.