Upper bounds on number fields of given degree and bounded discriminant
Robert J. Lemke Oliver, Frank Thorne · Duke Mathematical Journal · 2022
Let Nn(X) denote the number of degree n number fields with discriminant bounded by X. In this note, we improve the best-known upper bounds on Nn(X), finding that Nn(X)=O(Xc(logn)2) for an explicit constant c.