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An effective bound of p for algebraic points on Shimura curves of Γ₀(p)-type

100%

Arai K.

Acta Arithmetica

2014

tom 164

nr 4

343-353

In previous articles, we showed that for number fields in a certain large class, there are at most elliptic points on a Shimura curve of Γ₀(p)-type for every sufficiently large prime number p. In this article, we obtain an effective bound for such p.

Non-existence of points rational over number fields on Shimura curves

100%

Arai K.

Acta Arithmetica

2016

tom 172

nr 3

243-250

Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.

Points on X⁺₀(N) over quadratic fields

63%

Arai K., Momose F.

Acta Arithmetica

2012

tom 152

nr 2

159-173

Ograniczanie wyników

3 Acta Arithmetica

3 Arai K.

1 Momose F.

1 2016

1 2014

1 2012

Wyniki wyszukiwania

An effective bound of p for algebraic points on Shimura curves of Γ₀(p)-type

Non-existence of points rational over number fields on Shimura curves

Points on X⁺₀(N) over quadratic fields