Hilbert's Irreducibility Theorem and Ideal Class Groups of Quadratic Fields

Kaivalya Kulkarni; Aaron Levin

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arXiv · 2111.15582

Hilbert's Irreducibility Theorem and Ideal Class Groups of Quadratic Fields

Kaivalya Kulkarni·Aaron Levin

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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.

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Kaivalya Kulkarni, Aaron Levin. 2021-11-30. Hilbert's Irreducibility Theorem and Ideal Class Groups of Quadratic Fields. https://arxiv.org/abs/2111.15582

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