Algebraic Groups and Algebraic Dependence
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Publication:5556553
DOI10.2307/2373294zbMath0169.36701OpenAlexW2326124332WikidataQ100165378 ScholiaQ100165378MaRDI QIDQ5556553
Publication date: 1968
Published in: American Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2373294
Related Items (62)
On the algebraic dependence of holonomic functions ⋮ INVARIANT HYPERSURFACES ⋮ Necessary conditions for Liouvillian solutions of (third order) linear differential equations ⋮ Comments on Rosenlicht’s Integration in Finite Terms ⋮ On the computation of the parameterized differential Galois group for a second-order linear differential equation with differential parameters ⋮ On the algebraic properties of solutions of inhomogeneous hypergeometric equations ⋮ Submodules of products of quasi-periodic modules ⋮ Unipotent differential algebraic groups as parameterized differential Galois groups ⋮ Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence ⋮ On Ramis's solution of the local inverse problem of differential Galois theory ⋮ Autonomous functions ⋮ On the algebraic independence of values of generalized hypergeometric functions ⋮ Unnamed Item ⋮ Transcendental Liouvillian solutions of first order nonlinear differential equations ⋮ Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation ⋮ PILOT-WAVE HYDRODYNAMICS: QUANTISATION OF PARTIAL INTEGRABILITY FROM A NONLINEAR INTEGRO-DIFFERENTIAL EQUATION OF THE SECOND ORDER ⋮ Integration in finite terms with dilogarithmic integrals, logarithmic integrals and error functions ⋮ Integration in finite terms: dilogarithmic integrals ⋮ On the differential transcendentality of the Morita \(p\)-adic gamma function ⋮ Generalized differential Galois theory ⋮ Zero estimates on group varieties. I ⋮ Necessary conditions for super-integrability of Hamiltonian systems ⋮ A Galois-theoretic proof of the differential transcendence of the incomplete gamma function ⋮ DIFFERENCE ALGEBRAIC RELATIONS AMONG SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS ⋮ Difference Galois theory of linear differential equations ⋮ Solvable-by-finite groups as differential Galois groups ⋮ Differential Galois obstructions for integrability of homogeneous Newton equations ⋮ Integrability of Hamiltonian systems with homogeneous potentials of degrees \(\pm 2\). An application of higher order variational equations ⋮ Integration in finite terms with elementary functions and dilogarithms ⋮ Computing Galois groups of completely reducible differential equations ⋮ Linear forms in elliptic logarithms ⋮ Algebraic groups as difference Galois groups of linear differential equations ⋮ On the Constructive Inverse Problem in Differential Galois Theory# ⋮ Differential Galois theory of linear difference equations ⋮ Strong minimality and the \(j\)-function ⋮ Théories de Galois différentielles et transcendance ⋮ Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials ⋮ Moving subvarieties by endomorphisms ⋮ On algebraic identities between solution matrices of Bessel's and Kummer's equations ⋮ A note on symbolic integration with polylogarithms ⋮ A Lindemann-Weierstrass theorem for semi-abelian varieties over function fields ⋮ A structure theorem for the elementary functions and its application to the identity problem ⋮ Abelian extensions in Picard-Vessiot theory ⋮ Exponential sums over finite fields and differential equations over the complex numbers: Some interactions ⋮ On model complete differential fields ⋮ A new bound on Hrushovski’s algorithm for computing the Galois group of a linear differential equation ⋮ Differential Galois integrability obstructions for nonlinear three-dimensional differential systems ⋮ Estimating isogenies on elliptic curves ⋮ Algebraic independence of elementary functions and its application to Masser's vanishing theorem ⋮ The inverse Galois problem of extensions of difference fields ⋮ Some unlikely intersections beyond André–Oort ⋮ Calculating the Galois group of \(L_1(L_2(y))=0,\) \(L_1, L_2\) completely reducible operators ⋮ Unnamed Item ⋮ Differential Galois theory and isomonodromic deformations ⋮ Shidlovskii irreducibility ⋮ Fields of large transcendence degree generated by values of elliptic functions ⋮ When any three solutions are independent ⋮ Zero estimates on group varieties. II ⋮ Calculating the Galois group of \(Y'=AY+B\), \(Y'=AY\) completely reducible ⋮ Ideals generated by exponential-polynomials ⋮ On the measure of algebraic independence of certain values of elliptic functions ⋮ Finiteness theorems on hypersurfaces in partial differential-algebraic geometry
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