On the functional equation af \(Af^2 + Bg^2 = 1\) on the field of complex \(p\)-adic numbers

DOI10.1134/S207004661001005XzbMath1268.39027arXivmath/0508032OpenAlexW1980190522MaRDI QIDQ1760217

Eberhard Mayerhofer

Publication date: 13 November 2012

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508032

zbMATH Keywords

\(p\)-adic analysis\(p\)-adic differential equations\(p\)-adic functional equations

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Functional equations for functions with more general domains and/or ranges (39B52) Non-Archimedean function theory (30G06) Non-Archimedean valued fields (12J25)

Cites Work

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• On the equation 𝑓ⁿ+𝑔ⁿ=1
• A Note on the p-Adic Convergence of Solutions of Linear Differential Equations
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• A note on \(p\)-adic linear differential equations
• On the functional equation \[ \sum_{i=0}^ p a_ i f_ i^{n_ i} = 1 \]