We all know the well known Riemann hypothesis that the zeroes of the Riemann-zeta function have real part $\frac12$ seems to hold $($as far as I know$)$ for all prime numbers. I was curious if there were any arguments $($opinions, not proofs$)$ against this being true. I only have a basic background in analysis and complex analysis, but for me it is hard to imagine how the prime numbers could be connected to complex numbers.
2026-03-26 14:25:00.1774535100
Are there any arguments against the Riemann hypothesis?
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There are a few. It is generally believed that the theorem is true. Moreover, it has been shown to be true for many many numbers. There have been theorems which were shown to be false well beyond the computable range. So what is always needed is a formal proof or counterexample. For a good reference with arguments against Riemann, see this article.