Application of the \(p\)-adic topology on \(\mathbb{Z}\) to the problem of finding solutions in integers of an implicit linear difference equation

DOI10.1007/s10958-018-4072-xzbMath1404.39002OpenAlexW2895508108MaRDI QIDQ1755762

A. B. Goncharuk, V. A. Gerasimov, Sergey L. Gefter

Publication date: 11 January 2019

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-018-4072-x

zbMATH Keywords

\(p\)-adic topologyfirst order difference equation

Mathematics Subject Classification ID

Linear difference equations (39A06)

Related Items (4)

Implicit Linear Nonhomogeneous Difference Equation over ℤ with a Random Right-Hand Side ⋮ Analogue of the Cramer rule for an implicit linear second order difference equation over the ring of integers ⋮ Implicit linear first order difference equations over commutative rings ⋮ Uniqueness criterion and Cramer's rule for implicit higher order linear difference equations over \(\mathbf{Z} \)

Cites Work

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• Invertibility of linear difference operators with constant coefficients
• The Hurwitz product, \(p\)-adic topology on \(\mathbb{Z}\), and fundamental solution to linear differential equation in the ring \(\mathbb{Z}x\)
• Discrete time systems, operator models, and scattering theory
• On Solutions of Zero Exponential Type for Some Inhomogeneous Differential-Difference Equations in a Banach Space
• On Singular Implicit Linear Dynamical Systems
• Implicit linear difference equation in Frechet spaces

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