CHIGIRA Naoki Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (40292073)
SATO Motohiko Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (30254139)
TAKEGAHARA Yugen Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (10211351)
(1)Using the squared Moebius function for half-integral matrices defined by H.Katsurda result of 1, we gave an explicit formula for the Koecher-Maass Dirichlet series attached to the Klingen-Eisenstein lifting of even degree of an elliptic cuspidal Hecke-eigenform f.(Joint work with T.Ibukiyama.)In this explicit formula, there appears a certain Dirichlet series of two variables attached to f, which was originally investigated by W.Kohnen and D.Zagier. Furthermore, by using the same method, we gave also an explicit formula in the case of the Klingen-Eisenstein lifting of odd degree. In this formula, there appears a new type of Dirichlet series of two variables attached to f.
(2)T.Ikeda gave a generarization of the Saito-Kurokawa lifting of an elliptic cuspidal Hecke-eigenform f, and constructed a certain Siegel cusp form, called the Ikeda lifint of f. We gave an explicit formula for the Koecher-Maass series for the Ikeda lif of f.(Partly joint work with T.Ibukiyama.)
(3)We gave a good sufficient condition for two Siegel cuspidal Hecke-eigenforms to conincide with each other. Furthermore, we proposed a certain conjecture on a refinement of the above result, and proved this conjecture under a certain condition on the non-vanishing of the Koecher-Maass series.
(4)We proved that a zeta function of Andrianov type for the Siegel-Eisenstein series has Euler product, and determined a 'good' Euler factor of it.