Zeros of p-adic differential polynomials
Tóm tắt
Let
$$\mathbb{K}$$
be a complete algebraically closed p-adic field of characteristic zero. We consider a differential polynomial of the form F = a
n
f
n
f
(k) + a
n−1
f
n−1 + ... + a
0 where the a
j
are small functions with respect to f and f is a meromorphic function in
$$\mathbb{K}$$
or inside an open disk. Using p-adic methods, we can prove that when N(r, f) = S(r, f), then F must have infinitely many zeros, as in complex analysis.
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