Periods and congruence of modular forms, and Selmer group

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(1) We solved Ikeda's conjecture on the period of the Hermitian Ikeda lift.(2) We compute the special values of ceratain vector valued Siegel modular forms and confirmed a conjecture proposed by N. Dummigan (joint work with N. Dummigan and T. Ibukiyama). Moreover we computed the special values of the standard L-function of the Kim-Shahidi lift of Ramanujan delta function △, and confirmed that it is complatible with Zagier's conjecture on the special values of symmetric forth L function of △(joint work with T. Ibukiyama).(3) We established an algorithm for computing the special values of the triple L function of elliptic modular forms (joint work with T. Ibukiyama). By using it we considered the congruence between Ikeda-Miyawaki lift and non- Ikeda-Miyawaki lift (joint work with T. Ibukiyama, C. Poor, and D. Yuen).(4) We gave an explicit formula for the Fourier coefficient of the Poincare series for the congruence subgroup Γ_0 (N) of S_<p2>(Z).(5) We gave an explicit formula of twisted Koecher-Maass series of the Saito-Kurokawa lift. As an application we obtained a linear dependence of the special values of the Rankin-Selberg series of certain half-integral weight modular forms (joint work with Y. Mizuno). Moreover we gave an explicit formula of twisted Koecher-Maass series of the Duke-Imamoglu-Ikeda lift.(6) We consider congruence between the Klingen-Eisenstein series and cups forms (joint work with S. Mizumoto).