Research on automorphic forms

H.吉田研究了表示有限群的西格尔模形式的θ系列和广义赫克的理论。他计算了零的各种L-功能与自守形式。他还确定unitarizable主要系列表示完全为p进Chevalley群的经典类型。Hijikata证明了p-adic域上GL（2）的任意光滑不可约表示对各向异性环面的限制是多重自由的。他（与A.Pizer，T。Schemanske）在θ级数的经典基问题上得到了一个确定的结果，M.上田利用扭算子在半整权模形式上得到了一些有趣的结果。他的结果表明存在的理论的新形式也为半积分权的情况下。石井证明了一个标准的不存在的阿贝尔品种无处不在良好的减少。

H. Yoshida has investigated representations of finite groups on Siegel modular forms in terms of theta series and generalized Hecke's theory. He has calculated zeros of various L-functions associated with automorphic forms. He also determined unitarizable principal series representations completely for p-adic Chevalley groups of classical type.H. Hijikata has proved that the restriction to an anisotropic torus of an arbitrary smooth irreducible representation of GL(2) over a p-adic field is multiplicity free. He (with A.Pizer, T. Schemanske) has obtained a definitive result on the classical basis problem on theta series.M.Ueda has obtained interesting results on modular forms of half integral weight, using twisting poerators. His results suggest the existence of the theory of new forms also for the half integral weight case.H. Ishii proved a criterion for the non-existence of an abelian variety with everywhere good reduction.