A Note on p-adic Linear Differential Equations

Boutabaa, Abdelbaki

doi:10.1006/jnth.2000.2602

Search citation statements

Order By: Relevance

Paper Sections

Select...

Proof Of the Main Theorem1

Citation Types

Supporting

Mentioning

Contrasting

Unclassified

Year Published

2007

2020

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…with Q (2) not identically zero. We define the characteristic number of (E) as N (E) = max i=0,1,2 deg Q (i) − i, and the characteristic polynomial of (E) as…”

Section: Proof Of the Main Theoremmentioning

confidence: 99%

On the functional equation Af 2 + Bg 2 = 1 on the field of complex p-adic numbers

Mayerhofer

2010

P-Adic Num Ultrametr Anal Appl

View full text Add to dashboard Cite

For a fixed prime p, let Cp denote the complex p-adic numbers. For polynomials A, B ∈ Cp[x] we consider decompositions A(x)f 2 (x)+B(x)g 2 (x) = 1 of entire functions f, g on Cp and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide an independent proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa's method.

show abstract