Add to ORKG"Algebraic Number Theory and Related Topics 2015". November 30 - December 4, 2015. edited by Hiroki Takahashi, Yasuo Ohno and Takahiro Tsushima. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.In this survey, we summarize known results and the author's works concerning rational points on Shimura curves
Given a set S of elements in a number field k, we discuss the existence of planar algebraic curves o...
AbstractIt is proven that the cusps are the only points which are rational over Q on X0(N) for N = 5...
The main goal of this article is to give an explicit rigid analytic uniformization of the maximal to...
Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves $X_0(D,N)$. ...
"Algebraic Number Theory and Related Topics 2013". December 9～13, 2013. edited by Tadashi Ochiai, Ta...
AbstractIn this article, we prove that the Q-rational points on the modular curve X0+(37M) consist o...
Let X_B denote the Shimura curve defined by an indefinite rational quaternion division algebra B. By...
The j-function acts as a parametrization of the classical modular curve. Its values at complex multi...
Let XD be the Shimura curve associated with an indefinite rational quaternion algebra of reduced dis...
We complete the computation of all $\mathbb{Q}$-rational points on all the $64$ maximal Atkin-Lehner...
This thesis deals with rational points on elliptic curves. Darmon and Logan proposed a conjectural c...
This thesis explores one of the essential arithmetical and diophantine properties of Shimura curves ...
L'étude du nombre de points rationnels d'une courbe définie sur un corps fini se divise naturellemen...
This thesis is concerned with the problem of determining sets of rational points on algebraic curves...
We describe how the quadratic Chabauty method may be applied to explicitly determine the set of rati...
Given a set S of elements in a number field k, we discuss the existence of planar algebraic curves o...
AbstractIt is proven that the cusps are the only points which are rational over Q on X0(N) for N = 5...
The main goal of this article is to give an explicit rigid analytic uniformization of the maximal to...
Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves $X_0(D,N)$. ...
"Algebraic Number Theory and Related Topics 2013". December 9～13, 2013. edited by Tadashi Ochiai, Ta...
AbstractIn this article, we prove that the Q-rational points on the modular curve X0+(37M) consist o...
Let X_B denote the Shimura curve defined by an indefinite rational quaternion division algebra B. By...
The j-function acts as a parametrization of the classical modular curve. Its values at complex multi...
Let XD be the Shimura curve associated with an indefinite rational quaternion algebra of reduced dis...
We complete the computation of all $\mathbb{Q}$-rational points on all the $64$ maximal Atkin-Lehner...
This thesis deals with rational points on elliptic curves. Darmon and Logan proposed a conjectural c...
This thesis explores one of the essential arithmetical and diophantine properties of Shimura curves ...
L'étude du nombre de points rationnels d'une courbe définie sur un corps fini se divise naturellemen...
This thesis is concerned with the problem of determining sets of rational points on algebraic curves...
We describe how the quadratic Chabauty method may be applied to explicitly determine the set of rati...
Given a set S of elements in a number field k, we discuss the existence of planar algebraic curves o...
AbstractIt is proven that the cusps are the only points which are rational over Q on X0(N) for N = 5...
The main goal of this article is to give an explicit rigid analytic uniformization of the maximal to...