Browse > Article

FERMAT-TYPE EQUATIONS FOR MÖBIUS TRANSFORMATIONS  

Kim, Dong-Il (Department of Mathematics Hallym University)
Publication Information
Korean Journal of Mathematics / v.18, no.1, 2010 , pp. 29-35 More about this Journal
Abstract
A Fermat-type equation deals with representing a nonzero constant as a sum of kth powers of nonconstant functions. Suppose that $k{\geq}2$. Consider $\sum_{i=1}^{p}\;f_i(z)^k=1$. Let p be the smallest number of functions that give the above identity. We consider the Fermat-type equation for MAobius transformations and obtain $k{\leq}p{\leq}k+1$.
Keywords
Fermat-type equation; $M{\ddot{o}}bius$ transformation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 C.W. Curtis, Linear Algebra, Springer-Verlag, New York, 1984, 161-162.
2 H. Fujimoto, On meromorphic maps into the complex projective space, J. Math. Soc. Japan 26 (1974), 272-288.   DOI
3 M. Green Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math. 97 (1975), 43-75.   DOI   ScienceOn
4 G. Gundersen, Complex functional equations, Proceedings of the Summer School, Complex Differential and Functional Equations, Mekrijarvi 2000, ed. by Ilpo Laine, University of Joensuu, Department of Mathematics Report Series No. 5 (2003), 21-50.
5 W.K. Hayman, Waring's problem fur analytische Funktionen, Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. 1984 (1985), 1-13.
6 W.K. Hayman, The strength of Cartan's version of Nevanlinna theory, Bull. London Math. Soc. 36 (2004), 433-454.   DOI
7 D.-I. Kim, Waring's problem for linear polynomials and Laurent polynomials, Rocky Mountain J. Math. 35 (2005), no. 2, 1533-1553.   DOI
8 J. Molluzzo Monotonicity of quadrature formulas and polynomial representation, Doctoral thesis, Yeshiva University, 1972.
9 D. Newman and M. Slater, Waring's problem for the ring of polynomials, J. Number Theory 11 (1979), 477-487.   DOI
10 N. Toda, On the functional equation ${\Sigma}{^p_{i=0}a_if^{n_i}_i}$ = 1, Tohoku Math. J. 23 (1971), 289-299.   DOI