On the functional equation Af 2 + Bg 2 = 1 on the field of complex p-adic numbers
Tóm tắt
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) f
2 (x) + B (x) g
2 (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.
Tài liệu tham khảo
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