Abstract
A new Nevanlinna theorem on q p-adic small functions is given. Let f, g, be two meromorphic functions on a complete ultrametric algebraically closed field \({\mathbb{K}}\) of characteristic 0, or two meromorphic functions in an open disk of \({\mathbb{K}}\), that are not quotients of bounded analytic functions by polynomials. If f and g share 7 small meromorphic functions I.M., then \(f=g\). Better results hold when f and g satisfy some property of growth. Particularly, if f and g have finitely many poles or finitely many zeros and share 3 small meromorphic functions I.M., then \(f=g\).
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We are grateful to the anonymous referee for suggestions and improvements.
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This paper is dedicated to the memory of Professor Walter Hayman.
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Escassut, A., Yang, C.C. A short note on a pair of meromorphic functions in a p-adic field, sharing a few small ones. Rend. Circ. Mat. Palermo, II. Ser 70, 623–630 (2021). https://doi.org/10.1007/s12215-020-00519-0
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DOI: https://doi.org/10.1007/s12215-020-00519-0