主講者: 黃秀戀博士 (中研院數學所)
講題: On generalized Buchi's problem
時間: 2011-10-04 (Tue.)  14:30 - 15:30
地點: 數學所 617 研討室 (台大院區)
Abstract: Hilbert's Tenth Problem asks whether there is a general algorithm to determine, given any polynomial in several variables, whether there exists a zero with all coordinates in rational integers. It was proved in the negative by Yu. Matiyasevich in 1970. In the 70's J. R. Buchi was able to relate Hilbert's Tenth Problem to the following Diophantine problem: Buchi's square problem: Does there exist an integer $M>0$ such that all $x_1,...,x_M\in {\mathbb Z}$ satisfying the equations $ x_1^2-2x_2^2+x_3^2=x_2^2-2x_3^2+x_4^2=\cdots=x_{M-2}^2-2x_{M-1}^2+x_M^2=2 $ must also satisfy $x_i^2=(x+i)^2$ for a fixed integer $x$ and $i\in\{1,...,M\} $? A generalization of Buchi's square problem asks is there a positive integer $M$ such that any sequence $(x_1^n,...,x_M^n)$ of $n$-th powers of integers with $n$-th difference equal to $n!$ is necessarily a sequence of $n$-th powers of successive integers. In this talk, we discuss an analogue of this problem for meromorphic functions and algebraic functions.
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