Research on automorphic representations

H.Yoshida研究了Hilbert模形式的周期，并证明了Shimura关于P，Q-不变量的定理。他还研究了衍生物的阿丁的L-职能在s=0，并发现了一个关系时期的阿贝尔品种与复杂的乘法。T.Ikeda研究了Eisenstein级数的留数，并证明了Eisenstein级数不收敛时的Siegel-Weil型公式; K.Hiraga研究了一个离散级数表示的重数，使它出现在L^2（Gamma/G）中，其中G是半单李群，Gamma是离散子群。T.Umeda在quatum群的情况下研究了对偶约化对的概念; Hijikata证明了Dedekind整环的商域上半单代数的一个逼近定理;与这个猜想有关，他得到了许多关于序和格的结果。

H.Yoshida studied periods of Hilbert modular forms and proved Shimura's conjectures on P,Q-invariants. He also studied the derivatives of Artin's L-functions at s=0 and found a relation with periods of abelian varieties with complex multiplication. This relation can be sharpened by the notion of "absolute CM-periods".T.Ikeda studied residues of Eisenstein series and proved a Siegel-Weil type formula when Eisenstein series does not converge.K.Hiraga studied the multiplicity of a discrete series representation with which it occurs in L^2 (GAMMA/G), where G is a semisimple Lie group and GAMMA is a discrete subgroup.T.Umeda studied the notion of dual reductive pair in the case of quatum groups ; he generalized Capelli type identities for this case.H.Hijikata conjectured an approximation theorem for semisimple algebras over the quotient field of a Dedekind domain ; related with this conjecture, he obtained many results on orders and lattices.