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Bounds on the largest prime factor of a negative discriminant with one class per genus
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classification
math.NT
keywords
discriminantclassfactorgaussgenusleastnegativeprime
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It was conjectured by Gauss that any negative discriminant with at least 32 genera has at least two classes of binary quadratic forms in each genus. We prove that such a discriminant cannot have a particularly large prime factor, by an argument similar to that of Baker's solution to Gauss' class number one problem.
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