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I assume a number of results have been proven conditionally on the Riemann hypothesis, of course in number theory and maybe in other fields. What are the most relevant you know? It would also be nice ...

There are lots of known and interesting consequences of the Riemann Hypothesis being true. Are there any known and interesting consequences of the Riemann Hypothesis being false?

What are some examples of serious mathematical theory-building around hypotheses that are believed or known to be false? One interesting example, and the impetus for this question, is work in number ...

Hello, I've been interested in number theory for several years, and as time goes by, I read more and more articles in which theorems begin with "Assume the Riemann Hypothesis holds." But up to now, I ...