What difficult problem is deeply connected to the RH, such that ruling out its specific zeros is equivalent to proving a version of the RH concerning number fields?

Answer

Proving the non-existence of Landau–Siegel zeros.

The connection is deep, as ruling out the Landau–Siegel zeros is equivalent to proving a certain version of the Riemann Hypothesis specifically regarding number fields.

What difficult problem is deeply connected to the RH, such that ruling out its specific zeros is equivalent to proving a version of the RH concerning number fields?
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