Experts have long conjectured that any proof of the Riemann Hypothesis would apply for all Dirichlet L-functions too.
Hardy wrote exactly that in 1921 (image below).
Interestingly, OpenAI's 7/8 quasi-Riemann hypothesis actually cannot prove the result for only zeta!
The family-wide formulation is essential to the argument. The argument proves the bound simultaneously for all finite-order Hecke L-functions over Q[sqrt(-3)], and it has to do that to work. The generality is part of the proof itself.
So Hardy was quite right on this conjecture he made more than 100 years ago.
@iteratedlog @AlexKontorovich @jdlichtman @KenOno691 @wtgowers
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