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?
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

An explicit zero $\rho$ for $\zeta(s)$, off the critical line, would give an explicit lower bound on the class number $h(d)$ for $\mathbb Q(\sqrt{d})$, for a range of $d$ in terms of $\text{Im}(\rho)$. This is the 'DeuringHeilbronn phenomenon,' with results due to these two and others beginning in the 1930's. For an elementary account, see 


protected by Todd Trimble♦ Oct 2 at 11:57
Thank you for your interest in this question. Because it has attracted lowquality answers, posting an answer now requires 10 reputation on this site.
Would you like to answer one of these unanswered questions instead?