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Zeros of p-adic differential polynomials |
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| Authors: | A Escassut W Lü C C Yang |
| Institution: | 1. Laboratoire de Mathematiques, UMR 6620, Université Blaise Pascal Les Cézeaux, 63171, Aubiere, France 2. Department of Mathematics, China University of Petroleum, Qingdao, 266580, P.R. China 3. Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China |
| Abstract: | 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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