Counting $S_5$-fields with a power saving error term

Abstract

We show how the Selberg ${\Lambda }^2$-sieve can be used to obtain power saving error terms in a wide class of counting problems which are tackled using geometry of numbers. Specifically, we give such an error term for the counting function of $S_5$-quintic fields.

7 pages

References in corpus (2)

• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
• Most hyperelliptic curves over Q have no rational points

Cited by in corpus (1)

• Odd degree number fields with odd class number