[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b150600

ON FUNCTIONAL EQUATIONS OF THE FERMAT-WARING TYPE FOR NON-ARCHIMEDEAN VECTORIAL ENTIRE FUNCTIONS

An, Vu Hoai (Hai Duong College)
Ninh, Le Quang (Thai Nguyen University of Education)

Publication Information

Bulletin of the Korean Mathematical Society / v.53, no.4, 2016 , pp. 1185-1196 More about this Journal

Abstract

We show a class of homogeneous polynomials of Fermat-Waring type such that for a polynomial P of this class, if $P(f_1,{\ldots},f_{N+1})=P(g_1,{\ldots},g_{N+1})$ , where $f_1,{\ldots},f_{N+1}$ ; $g_1,{\ldots},g_{N+1}$ are two families of linearly independent entire functions, then $f_i=cg_i$ , $i=1,2,{\ldots},N+1$ , where c is a root of unity. As a consequence, we prove that if X is a hypersurface defined by a homogeneous polynomial in this class, then X is a unique range set for linearly non-degenerate non-Archimedean holomorphic curves.

Keywords

Diophantine equations; non-Archimedean field; unique range sets; holomorphic curves;

Citations & Related Records

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