• Title, Summary, Keyword: non-Archimedean field

Search Result 2, Processing Time 0.027 seconds

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

  • An, Vu Hoai;Ninh, Le Quang
    • Bulletin of the Korean Mathematical Society
    • /
    • v.53 no.4
    • /
    • pp.1185-1196
    • /
    • 2016
  • 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.