INTEGRAL POINTS ON THE CHEBYSHEV DYNAMICAL SYSTEMS
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초록
Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let α0 ∈ A1(K) ⊂ P1(K) and let Γ0 be the set of the images of α0 under especially all Chebyshev morphisms. Then for any α ∈ A1(K), we show that there are only a finite number of elements in Γ0 which are S-integral on P1 relative to (α). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on P1, which generalizes the above finiteness result for Chebyshev morphisms.
Abstract
Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let α0 ∈ A1(K) ⊂ P1(K) and let Γ0 be the set of the images of α0 under especially all Chebyshev morphisms. Then for any α ∈ A1(K), we show that there are only a finite number of elements in Γ0 which are S-integral on P1 relative to (α). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on P1, which generalizes the above finiteness result for Chebyshev morphisms.
참고문헌 (7)
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