PM013 492 pages ISBN 2921120089 1992 
Robert P. Langlands and Dinakar Ramakrishnan, editorsAlthough they are central objects in the theory of diophantine equations, the zetafunctions of Hasse–Weil are not well understood. One large class of varieties whose zetafunctions are perhaps within reach are those attached to discrete groups, and called generically Shimura varieties. The techniques involved are difficult: representation theory and harmonic analysis; the trace formula and endoscopy; intersection cohomology and L^{2}cohomology; and abelian varieties with complex multiplication. The simplest Shimura varieties for which all attendant problems occur are those attached to unitary groups in three variables over imaginary quadratic fields, referred to in the present volume as Picard modular surfaces. In an attempt to render this very new domain accessible to mathematicians in related fields and to students, the contributors have provided a coherent and thorough account of the necessary ideas and techniques, many of them novel and not previously published, and of some applications. Contents

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