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I like the phrase "only need the grand Riemann hypothesis"... One of my favorite results known contingent on this result (rather, the weaker generalized Riemann hypothesis), is that the ring of integers in a number field (EDIT: with infinite unit group) is Euclidean with respect to some Euclidean algorithm if an only if is is a PID. Interestingly, the "amount" of GRH needed here far exceeds that of the field in question. One must assume GRH for an infinite number of extension fields as well. |
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Post Made Community Wiki by S. Carnahan♦
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I like the phrase "only need the grand Riemann hypothesis"... One of my favorite results known contingent on this result (rather, the weaker generalized Riemann hypothesis), is that the ring of integers in a number field is Euclidean with respect to some Euclidean algorithm if an only if is is a PID. Interestingly, the "amount" of GRH needed here far exceeds that of the field in question. One must assume GRH for an infinite number of extension fields as well. |
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