Automorphic Forms of Several Variables: Taniguchi Symposium, Katata, 1983

Description

This volume contains papers based on the 13th Taniguchi Symposium, which focused on the geometric aspect of the theory of automorphic forms of several variables. These papers cover such topics as Eisenstein series, Hilbert and Siegel modular varieties, dimension formulae for the space of automorphic forms, and families of abelian varieties. Other papers present more number-theoretic viewpoints - arithmetic automorphic forms, Shimura varieties, and p-adic group representations - reflecting recent developments in this field. A testimony to the richness and breadth of the modern theory of automorphic functions, this volume is a valuable addition to the research library. CONTENTS Preface List of Participants T. Arakawa, On certain automorphic forms of Sp(l, q) W. L. Baily, Jr., Arithmetic Hilbert modular forms E. Freitag, Holomorphic tensors on subvarieties of the Siegel modular variety 93 P. B. Garrett, Pullbacks of Eisenstein series; applications 114 M. Harris, Arithmetic vector bundles on Shimura varieties 138 H. Hijikata, Some supercuspida1 representations induced from parahoric subgroups 160 M. L. Karel, Special values of elliptic modular forms 179 H. Klingen, On Eisenstein series and some applications 226 S. S. Kudla, Seesaw dual reductive pairs 244 Chemistry and GTFABV's Analytic representations of SL 2 over a p-adic number field, II T. Oda, Distinguished cycles and Shimura varieties M. Ohta, Hilbert modular forms of weight one and Galois representations I. Satake, On numerical invariants of arithmetic varieties of Q-rank one Y.-s. Tai, P1uri-canonica1 differentials of Hilbert modular varieties 370 R. Tsushima, An explicit dimension formula for the spaces of generalized automorphic forms with respect to Sp(2, Z) 378