Korean Journal of Mathematics

  • 제18권1호
  • /
  • Pages.29-35
  • /
  • 2010
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

FERMAT-TYPE EQUATIONS FOR MÖBIUS TRANSFORMATIONS

  • Kim, Dong-Il (Department of Mathematics Hallym University)
  • 투고 : 2009.12.16
  • 심사 : 2010.02.04
  • 발행 : 2010.03.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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 $k{\leq}p{\leq}k+1$.

키워드

참고문헌

  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. https://doi.org/10.2969/jmsj/02620272
  3. M. Green Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math. 97 (1975), 43-75. https://doi.org/10.2307/2373660
  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. https://doi.org/10.1112/S0024609304003418
  7. D.-I. Kim, Waring's problem for linear polynomials and Laurent polynomials, Rocky Mountain J. Math. 35 (2005), no. 2, 1533-1553. https://doi.org/10.1216/rmjm/1181069650
  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. https://doi.org/10.1016/0022-314X(79)90027-1
  10. N. Toda, On the functional equation ${\Sigma}{^p_{i=0}a_if^{n_i}_i}$ = 1, Tohoku Math. J. 23 (1971), 289-299. https://doi.org/10.2748/tmj/1178242646