2005•Annals of MathematicsOpen access

The density of discriminants of quartic rings and fields

Manjul Bhargava

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Abstract

The primary purpose of this article is to prove the following theorem. Theorem 1. Let N (i)4 (ξ, η) denote the number of S4-quartic fields K having 4 − 2i real embeddings such that ξ < Disc(K) < η. Then

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What this paper is about

The primary purpose of this article is to prove the following theorem. Theorem 1. Let N (i)4 (ξ, η) denote the number of S4-quartic fields K having 4 − 2i real embeddings such that ξ < Disc(K) < η. Then

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Available abstract

The primary purpose of this article is to prove the following theorem. Theorem 1. Let N (i)4 (ξ, η) denote the number of S4-quartic fields K having 4 − 2i real embeddings such that ξ < Disc(K) < η. Then

Key concepts: Mathematics, Quartic function, Pure mathematics

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