On the functional equation Af2 + Bg2 = 1 on the field of complex p-adic numbers

Eberhard Mayerhofer

doi:10.1134/S207004661001005X

On the functional equation Af² + Bg² = 1 on the field of complex p-adic numbers

Eberhard Mayerhofer

Vienna University of Economics and Business

Research output: Contribution to journal › Article › peer-review

Abstract

For a fixed prime p, let C_p denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f² (x) + B (x) g² (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa’s method.

Original language	English
Pages (from-to)	68-76
Number of pages	9
Journal	P-Adic Numbers, Ultrametric Analysis, and Applications
Volume	2
Issue number	1
DOIs	https://doi.org/10.1134/S207004661001005X
Publication status	Published - 1 Jan 2010
Externally published	Yes

Keywords

p-adic analysis
p-adic differential equations
p-adic functional equations

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10.1134/S207004661001005X

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abstract = "For a fixed prime p, let Cp denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f2 (x) + B (x) g2 (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa{\textquoteright}s method.",

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AB - For a fixed prime p, let Cp denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f2 (x) + B (x) g2 (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa’s method.

KW - p-adic analysis

KW - p-adic differential equations

KW - p-adic functional equations

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On the functional equation Af² + Bg² = 1 on the field of complex p-adic numbers

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Keywords

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