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- Title
A new bound for an extension of Mason's theorem for functions of several variables.
- Authors
M. Bayat; H. Teimoori
- Abstract
In this paper, using the generalized Wronskian, we obtain a new sharp bound for the generalized Mason?s theorem [1] for functions of several variables. We also show that the Diophantine equation (The generalized Fermat-Catalan equation) $$ a_{1}^{m_1} + a_{2}^{m_2} + \cdots + a_{n-1}^{m_{n-1}} = a_{n}^{m_{n}}, $$ where $ a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{C}[x_{1}, \ldots, x_{l}] $ , such that k out of the n-polynomials $ (k \leq n-2) $ are constant, and $ m_{1}, m_{2}, \ldots, m_{n} \in \mathbb{N}, $ under certain conditions for $ a_{i}(i = 1, \ldots, n) $, has no non-constant solution.
- Subjects
WRONSKIAN determinant; ALGEBRAIC functions; MATHEMATICAL variables; DIFFERENTIAL equations
- Publication
Archiv der Mathematik, 2004, Vol 82, Issue 3, p230
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-003-4827-5