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On rational torsion points of central ℚ -curves

Fumio Sairaiji;  Takuya Yamauchi — 2008

Journal de Théorie des Nombres de Bordeaux

Let E be a central ℚ -curve over a polyquadratic field k . In this article we give an upper bound for prime divisors of the order of the k -rational torsion subgroup E t o r s ( k ) (see Theorems 1.1 and 1.2). The notion of central ℚ -curves is a generalization of that of elliptic curves over ℚ . Our result is a generalization of Theorem 2 of Mazur [], and it is a precision of the upper bounds of Merel [] and Oesterlé [].

An explicit computation of p -stabilized vectors

Michitaka MIYAUCHI;  Takuya YAMAUCHI — 2014

Journal de Théorie des Nombres de Bordeaux

In this paper, we give a concrete method to compute p -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over p -adic fields. An application to the global setting is also discussed. In particular, we give an explicit p -stabilized form of a Saito-Kurokawa lift.

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