Number Theory Seminar
Wednesday, March 8, 2017, 3:15pm, 119 Physics
Silas Johnson (Northwestern)
Counting Functions, Mass Formulas, and Heuristics for Number Fields
Abstract:- The Malle-Bhargava heuristics give asymptotic predictions for the density of number fields of bounded discriminant with a given Galois group G, in terms of the number of G-extensions of p-adic fields Q_p. These heuristics can also be applied when the discriminant is replaced by any of a wide variety of other counting functions. Ill discuss how some of these alternate counting functions are built, the idea of global mass formulas, and some cases in which the heuristic predictions can be compared to known results. [video]
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