Ober­se­mi­nar "Num­ber Theo­ry and Arith­me­ti­cal Sta­ti­stics": Prof. Dr. Jür­gen Klü­ners (Pa­der­born), Asym­pto­tics of nil­po­tent ex­ten­si­ons of num­ber fields

Ort: A3.339
Veranstalter: Prof. Dr. Jürgen Klüners

Titel: Asymptotics of nilpotent extensions of number fields

Abstract: We give an overview about the proof of the weak Malle conjecture for nilpotent groups. Given a group G and a number field k, Malle defines a counting function.

Z(k,G;x) which counts all (finitely many) number fields with Galois group G and norm of the discriminant bounded by x. Malle conjectures that this counting function is
O(x^a * log(x)), where a(G) and b(k,G) are explicit constants. In the weak version we show the correctness of the constant a(G).