Septic Fields with Discriminant ±23

Septic fields with discriminant +- 2a3b

A targeted Martinet search

Constructing number fields with prescribed ramification is an important problem in computational number theory. In this paper, we consider the problem of computing all imprimitive number fields of a given degree which are unramified outside of a given finite set of primes S by combining the techniques of targeted Hunter searches with Martinet’s relative version of Hunter’s theorem. We then carr...

Application of Discriminant Analysis for Studying the Source Rock Potential of Probable Formations in the Lorestan Basin, Iran

Understanding the performance and role of each formation in a petroleum play is crucial for the efficient and precise exploration and exploitation of trapped hydrocarbons in a sedimentary basin. The Lorestan basin is one of the most important hydrocarbon basins of Iran, and it includes various oil-prone potential source rocks and reservoir rocks. Previous geochemical studies of the basin were n...

Progress towards Counting D5 Quintic Fields

Let N(5, D5, X) be the number of quintic number fields whose Galois closure has Galois group D5 and whose discriminant is bounded by X. By a conjecture of Malle, we expect that N(5, D5, X) ∼ C · X 1 2 for some constant C. The best known upper bound is N(5, D5, X) X 3 4, and we show this could be improved by counting points on a certain variety defined by a norm equation; computer calculations g...

Enumeration of Totally Real Number Fields of Bounded Root Discriminant

We enumerate all totally real number fields F with root discriminant δF ≤ 14. There are 1229 such fields, each with degree [F : Q] ≤ 9. In this article, we consider the following problem. Problem 1. Given B ∈ R>0, enumerate the set NF (B) of totally real number fields F with root discriminant δF ≤ B, up to isomorphism. To solve Problem 1, for each n ∈ Z>0 we enumerate the set NF (n,B) = {F ∈ NF...