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 ≤ 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 = ∫ 0 ∞ 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...