On degrees of three algebraic numbers with zero sum or unit product

Paulius Drungilas; Artūras Dubickas

Displaying similar documents to “On degrees of three algebraic numbers with zero sum or unit product”

On the Galois structure of algebraic integers and S-units.

T. Chinburg (1983)

Inventiones mathematicae

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On metacyclic extensions

Masanari Kida (2012)

Journal de Théorie des Nombres de Bordeaux

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Galois extensions with various metacyclic Galois groups are constructed by means of a Kummer theory arising from an isogeny of certain algebraic tori. In particular, our method enables us to construct algebraic tori parameterizing metacyclic extensions.

On the envelope of a vector field

Bernard Malgrange (2011)

Banach Center Publications

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Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.

The Algebraic Degree of Geometric Optimization Problems.

C. Bajaj (1988)

Discrete & computational geometry

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Solvable-by-finite groups as differential Galois groups

Claude Mitschi, Michael F. Singer (2002)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Remarks on the intrinsic inverse problem

Daniel Bertrand (2002)

Banach Center Publications

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The intrinsic differential Galois group is a twisted form of the standard differential Galois group, defined over the base differential field. We exhibit several constraints for the inverse problem of differential Galois theory to have a solution in this intrinsic setting, and show by explicit computations that they are sufficient in a (very) special situation.

Galois covers with prescribed fibers : the Beckmann-Black problem

Pierre Dèbes (1999)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Recent work on differential Galois theory

Marius Van der Put (1997-1998)

Séminaire Bourbaki

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On double covers of the generalized alternating group $ℤ_{d} ≀_{m}$ as Galois groups over algebraic number fields

Martin Epkenhans (1997)

Acta Arithmetica

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Let $ℤ_{d} ≀$ m $b e t h e g e n e r a l i z e d a l t e r n a t i n g g r o u p . W e p r o v e t h a t a l l d o u b l e c o v e r s o f$ ℤd ≀ m $o c c u r a s G a l o i s g r o u p s o v e r a n y a l g e b r a i c n u m b e r f i e l d . W e f u r t h e r r e a l i z e s o m e o f t h e s e d o u b l e c o v e r s a s t h e G a l o i s g r o u p s o f r e g u l a r e x t e n s i o n s o f ℚ (T) . I f d i s o d d a n d m > 7, t h e n e v e r y c e n t r a l e x t e n s i o n o f$ ℤd ≀ m $o c c u r s a s t h e G a l o i s g r o u p o f a r e g u l a r e x t e n s i o n o f ℚ (T) . W e f u r t h e r i m p r o v e s o m e o f o u r e a r l i e r r e s u l t s c o n c e r n i n g d o u b l e c o v e r s o f t h e g e n e r a l i z e d s y m m e t r i c g r o u p$ ℤd ≀ m $.$

The totally real $A_{6}$ extension of degree 6 with minimum discriminant.

Ford, David, Pohst, Michael (1993)

Experimental Mathematics

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Reduction of differential equations

Krystyna Skórnik, Joseph Wloka (2000)

Banach Center Publications

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Let (F,D) be a differential field with the subfield of constants C (c ∈ C iff Dc=0). We consider linear differential equations (1) $L y = D^{n} y + a_{n - 1} D^{n - 1} y + . . . + a_{0} y = 0$ , where $a_{0}, . . ., a_{n} \in F$ , and the solution y is in F or in some extension E of F (E ⊇ F). There always exists a (minimal, unique) extension E of F, where Ly=0 has a full system $y_{1}, . . ., y_{n}$ of linearly independent (over C) solutions; it is called the Picard-Vessiot extension of F E = PV(F,Ly=0). The Galois group G(E|F) of an extension field E ⊇ F consists of all differential automorphisms...