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 the geometry of numbers. Specifically, we give such an error term for the counting function of $S_5$ -quintic fields.

Keywords

• primary 13N15; secondary 16S36
• 16W55.