An explicit integral polynomial whose splitting field has Galois group $W(\mathbf{E}_8)$

Florent Jouve; Emmanuel Kowalski; David Zywina

Displaying similar documents to “An explicit integral polynomial whose splitting field has Galois group $W (E_{8})$ ”

Random Galois extensions of Hilbertian fields

Lior Bary-Soroker, Arno Fehm (2013)

Journal de Théorie des Nombres de Bordeaux

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Let $L$ be a Galois extension of a countable Hilbertian field $K$ . Although $L$ need not be Hilbertian, we prove that an abundance of large Galois subextensions of $L / K$ are.

Actions of the additive group $G_{a}$ on certain noncommutative deformations of the plane

Ivan Kaygorodov, Samuel A. Lopes, Farukh Mashurov (2021)

Communications in Mathematics

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We connect the theorems of Rentschler [] and Dixmier [] on locally nilpotent derivations and automorphisms of the polynomial ring $A_{0}$ and of the Weyl algebra $A_{1}$ , both over a field of characteristic zero, by establishing the same type of results for the family of algebras $A_{h} = 〈 x, y ∣ y x - x y = h (x) 〉,$ where $h$ is an arbitrary polynomial in $x$ . In the second part of the paper we consider a field $𝔽$ of prime characteristic and study $𝔽 [t]$ comodule algebra structures on $A_{h}$ . We also compute the Makar-Limanov invariant of absolute...

Counting discriminants of number fields

Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (2006)

Journal de Théorie des Nombres de Bordeaux

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For each transitive permutation group $G$ on $n$ letters with $n \leq 4$ , we give without proof results, conjectures, and numerical computations on discriminants of number fields $L$ of degree $n$ over $ℚ$ such that the Galois group of the Galois closure of $L$ is isomorphic to $G$ .

An integral transform and its application in the propagation of Lorentz-Gaussian beams

A. Belafhal, E.M. El Halba, T. Usman (2021)

Communications in Mathematics

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The aim of the present note is to derive an integral transform $I = \int_{0}^{\infty} x^{s + 1} e^{- β x^{2} + γ x} M_{k, ν} (2 ζ x^{2}) J_{μ} (χ x) d x,$ involving the product of the Whittaker function $M_{k, ν}$ and the Bessel function of the first kind $J_{μ}$ of order $μ$ . As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters $k$ and $ν$ of the Whittaker function. Eventually, we show the application of the integral in the propagation of hollow higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system...

Displaying similar documents to “An explicit integral polynomial whose splitting field has Galois group W ( E 8 ) ”

Random Galois extensions of Hilbertian fields

Actions of the additive group G a on certain noncommutative deformations of the plane

Counting discriminants of number fields

An integral transform and its application in the propagation of Lorentz-Gaussian beams

Displaying similar documents to “An explicit integral polynomial whose splitting field has Galois group $W (E_{8})$ ”

Actions of the additive group $G_{a}$ on certain noncommutative deformations of the plane