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Department of Mathematics pres.

Group, Lie and Number Theory Seminar

NT RTG Lectures II: Governing fields and statistics for 8-class ranks

The following result predates our work: given a positive integer d, there is a finite Galois extension M_d of Q so that, for any prime p not dividing 2d, the 2-, 4-, and 8-class ranks of Q(\sqrt{-dp}) are determined from the Artin symbol of p in Gal(M_d/Q). Starting from this result, we will give two approaches to finding statistics for 8-class ranks in families of imaginary quadratic fields. The first of these will directly use the governing fields M_d, while the latter will use a combinatorial trick to replace M_d with a field of smaller discriminant. Speaker(s): Alexander Smith (Harvard University)

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