Sometimes effective Thue-Siegel-Roth-Schmidt-Nevanlinna bounds, or better

DOI10.1016/0022-314X(85)90061-7zbMath0575.10032OpenAlexW2089636200MaRDI QIDQ1064341

Charles F. Osgood

Publication date: 1985

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-314x(85)90061-7

zbMATH Keywords

rational functionsalgebraic differential equationmeromorphic functionsNevanlinna Theoryapproximation of formal power serieseffectively computable lower boundsfirst proof of Nevanlinna's conjecturegeneralization of the n small function theoremsolutions to linear differential equationsThue-\(Siegel\)-\(Roth\)-\(Schmidt\) Theorem

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Approximation by rational functions (41A20) Abstract differential equations (12H20) Diophantine approximation, transcendental number theory (11J99)

Related Items (38)

Product type bounds on the approximation of values of E- and G-functions ⋮ Defective functions of meromorphic functions in the unit disc ⋮ Meromorphic points on curves ⋮ On meromorphic functions that share three values of finite weights ⋮ An extension of the theorem of Steinmetz-Nevanlinna to holomorphic curves ⋮ An analogue of continued fractions in number theory for Nevanlinna theory ⋮ An effective Roth's theorem for function fields ⋮ Sharp forms of Nevanlinna's error terms ⋮ The error term in Nevanlinna theory ⋮ An effective function field version of Schmidt's subspace theorem for projective varieties, with arbitrary families of homogeneous polynomials ⋮ Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties ⋮ Schmidt’s subspace theorem for moving hypersurfaces in subgeneral position ⋮ A lemma on the difference quotients ⋮ A generalization of the subspace theorem for higher degree polynomials in subgeneral position ⋮ Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem ⋮ On a General Form of the Second Main Theorem ⋮ Meromorphic functions of finite order with maximal deficiency sum ⋮ On Nevanlinna's error terms ⋮ Integral points of \(\mathbb{P}^ n-\{2n+1\) hyperplanes in general position\(\}\) ⋮ Height uniformity for integral points on elliptic curves ⋮ A sharp form of Nevanlinna's second fundamental theorem ⋮ A weak effective Roth's theorem over function fields ⋮ Three approaches to detecting discrete integrability ⋮ Schmidt's subspace theorem for moving hypersurface targets ⋮ Nevanlinna theory, Diophantine approximation, and numerical analysis. ⋮ The second main theorem for small functions and related problems ⋮ Approximation of real numbers with rational number sequences ⋮ Value distribution theory and Diophantine approximation ⋮ ON THE TRUNCATED SMALL FUNCTION THEOREM IN NEVANLINNA THEORY ⋮ The error term in Nevanlinna theory. II ⋮ Deficient rational functions and Ahlfors's theory of covering surfaces ⋮ Cartan's conjecture for moving hypersurfaces ⋮ Roth's theorem over arithmetic function fields ⋮ On the torsion values for sections of an elliptic scheme ⋮ Subspace theorem for moving hypersurfaces and semi-decomposable form inequalities ⋮ Quantitative subspace theorem and general form of second main theorem for higher degree polynomials ⋮ On the growth of the logarithmic derivative ⋮ The second main theorem for moving targets

Cites Work

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• Value distribution under analytic mappings of arbitrary Riemann surfaces
• Diophantine approximation
• Nearly perfect systems and effective generalizations of Shidlovski's theorem
• The lemma of the logarithmic derivative in several complex variables
• Second main theorem without exceptional intervals on arbitrary Riemann surfaces
• Meromorphic functions and conformal metrics on Riemann surfaces
• Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations
• Rational Approximation to Solutions of Algebraic Differential Equations
• A Measure of Linear Independence for Some Exponential Functions II
• Formal Solutions of Irregular Linear Differential Equations. Part I
• Computable Algebra, General Theory and Theory of Computable Fields

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