Degree of independence in non-archimedean fields
-
Pratchayaporn Doemlim
and
Tuangrat Chaichana
Abstract
The concept of degree independence, in the real number case, introduced in our earlier work is extended to non-archimedean fields. A sufficient condition for such independence is proved. As applications, sufficient conditions for degree independence of (i) elements in the field of formal Laurent series represented by Ruban continued fractions and of (ii) p-adic numbers are derived.
(Communicated by István Gaál)
References
[1] Browkin, J.: Continued fractions in local fields, I, Demonstratio Math. XI(1) (1978), 67–82.Search in Google Scholar
[2] Bugeau, Y.: Approximation by Algebraic Numbers, Cambridge University Press, Cambridge, 2004.Search in Google Scholar
[3] Bundschuh, P.—Wallisser, R.: Algebraische Unabhängigkeit P-adischer Zahlen, Math. Ann. 221 (1976), 243–249.Search in Google Scholar
[4] Bundschuh, P.: Transzendenzmasse in Körpern formaler Laurentreihen, J. Reine Angew. Math. 299/300 (1978), 411–432.Search in Google Scholar
[5] Bundschuh, P.—Chirskii, V. G.: Algebraic independence of elemens from ℂp over ℚp, I, Arch. Math. (Basel) 79 (2002), 345–352.Search in Google Scholar
[6] Bundschuh, P.—Chirskii, V. G.: Algebraic independence of elemens from ℂp over ℚp, II, Acta Arithmetica 113(40) (2004), 309–326.Search in Google Scholar
[7] Cassels, J. W. S.: Local Fields, Cambridge University Press, Cambridge, 1986.Search in Google Scholar
[8] Chaichana, T.—Komatsu, T—Laohakosol, V.: Liouville number in the non-archimedean case, Publ. Math. Debrecen 77(1–2) (2010), 39–63.Search in Google Scholar
[9] Fel’dman, N. I.: Estimate for a linear form of logarithms of algebraic numbers, Mat. Sbornik (N.S.) 76 (1968), 304–319 (in Russian); Engl. transl.: Math. USSR-Sb. 5 (1968), 291–307.Search in Google Scholar
[10] Müller, J.: Algebraische Unabhängigkeit der werte gewisser Lückenreihen in nicht-archimedisch bewerteten Körpern, Results Math. 24 (1993), 288–297.Search in Google Scholar
[11] Rattanamoong, J.—Laohakosol, V.: Degree of independence of numbers, Math. Slovaca 71(3) (2021), 615–626.Search in Google Scholar
© 2025 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
- Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
- Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
