Hilbert’s Irreducibility Theorem andideal class groups of quadratic fields
Volume 205 / 2022
Acta Arithmetica 205 (2022), 371-380
MSC: Primary 11R29; Secondary 12E25.
DOI: 10.4064/aa211224-22-9
Published online: 3 November 2022
Abstract
We prove a version of Hilbert’s Irreducibility Theorem in the quadratic case, giving a quantitative improvement to a result of Bilu–Gillibert in this restricted setting. As an application, we give improvements to several quantitative results counting quadratic fields with certain types of ideal class groups. The proof of the main theorem is based on a result of Stewart and Top on values of binary forms modulo squares.
