I noticed in many papers, it’s common to assume the Riemann Hypothesis or variants thereof in order to get their results. There will be an “optimal” bound where RH is true, and one that is easier to obtain but not conditional. And I’ve seen other conjectures of this kind:
- Riemann Hypothesis
- Lindelöf Hypothesis
- Generalized Riemann Hypothesis
- Ramanujan Conjecture
These are conjectures that are likely to be true. I think these assumptions are very deep and not to be taken for granted. It almost seems there are two number theories… one where the Riemann Hypothesis is true and one in which it’s merely conjectural.
So when and why do Number Theorists feel it’s okay to assume RH.
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