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7 papers · 1 filter
The derivative formula of -adic -functions for imaginary quadratic fields at trivial zeros
Masataka Chida, Ming-Lun Hsieh
The rank one Gross conjecture for Deligne-Ribet -adic -functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modula…
Inner product formula for Yoshida lifts
Ming-Lun Hsieh, Kenichi Namikawa
We prove an explicit inner product formula for vector-valued Yoshida lifts. As a consequence, we obtain the non-vanishing of Yoshida lifts.
The cyclotomic Iwasawa main conjecture for Hilbert cuspforms with complex multiplication
Takashi Hara, Tadashi Ochiai
We deduce the cyclotomic Iwasawa main conjecture for Hilbert modular cuspforms with complex multiplication from the multivariable main conjecture for CM number fields. To this end,…
Points on Shimura curves rational over imaginary quadratic fields in the non-split case
Keisuke Arai
For an imaginary quadratic field of class number , we prove that there are only finitely many isomorphism classes of rational indefinite quaternion division algebras su…
Non-existence of points rational over number fields on Shimura curves
Keisuke Arai
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 expand their r…
On the Rasmussen-Tamagawa conjecture for QM-abelian surfaces
Keisuke Arai
In the previous article, we showed the Rasmussen-Tamagawa conjecture for QM-abelian surfaces over imaginary quadratic fields. In this article, we generalize the previous work to QM…