Research on automorphic forms

H. Yoshida研究了有限群在西格尔模形式上的表示，用theta级数和广义Hecke理论。他计算了与自同构形式相关的各种l函数的零点。他还完全确定了经典类型h的p进Chevalley群的可一元主级数表示。Hijikata证明了在p进域上GL(2)的任意光滑不可约表示的各向异性环面的限制是无多重性的。他（与a . pizer， T. Schemanske）在级数的经典基问题上得到了一个确定的结果。m.u eda利用扭转算子在半积分权的模形式上得到了有趣的结果。他的结果表明，对于半积分权情况，也存在新形式理论。石井证明了处处具有良好约化的阿贝尔变体不存在的判据。

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.