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        Algebraic points on the projective line

        Su-ion Ih 대한수학회 2008 대한수학회지 Vol.45 No.6

        Schanuel’s formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of P1. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on P1 according as the height bound goes to ∞. Schanuel’s formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of P1. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on P1 according as the height bound goes to ∞.

      • KCI등재

        INTEGRAL POINTS ON THE CHEBYSHEV DYNAMICAL SYSTEMS

        Su-ion Ih 대한수학회 2015 대한수학회지 Vol.52 No.5

        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.

      • SCIESCOPUSKCI등재

        INTEGRAL POINTS ON THE CHEBYSHEV DYNAMICAL SYSTEMS

        IH, SU-ION Korean Mathematical Society 2015 대한수학회지 Vol.52 No.5

        Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let ${\alpha}_0{\in}{\mathbb{A}}^1(K){\subset}{\mathbb{P}}^1(K)$ and let ${\Gamma}_0$ be the set of the images of ${\alpha}_0$ under especially all Chebyshev morphisms. Then for any ${\alpha}{\in}{\mathbb{A}}^1(K)$, we show that there are only a finite number of elements in ${\Gamma}_0$ which are S-integral on ${\mathbb{P}}^1$ relative to (${\alpha}$). 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 ${\mathbb{P}}^1$, which generalizes the above finiteness result for Chebyshev morphisms.

      • SCIESCOPUSKCI등재

        ALGEBRAIC POINTS ON THE PROJECTIVE LINE

        Ih, Su-Ion Korean Mathematical Society 2008 대한수학회지 Vol.45 No.6

        Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

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