ENGLISH

The Zeta Functions of Picard Modular Surfaces

By Dinakar Ramakrishnan , Robert P. Janglands

Book information

Publisher
Centre De Recherches Mathematiques
Year
1992
ISBN
2921120089, 9782921120081
Language
english
Format
DJVU
Filesize
7 MB (6865800 bytes)
Pages
0\514
DPI
600
Orientation
portrait
Scanned
yes
Time added
2016-07-28 13:02:40
Algebraic Geometry;Geometry & Topology;MathematicsUsed & Rental Textbooks;Specialty BoutiqueUsed & Rental Textbooks;Specialty Boutique;Geometr

Description

Although they are central objects in the theory of diophantine equations, the zeta-functions of Hasse-Weil are not well understood. One large class of varieties whose zeta-functions are perhaps within reach are those attached to discrete groups, generically called Shimura varieties. The techniques involved are difficult: representation theory and harmonic analysis; the trace formula and endoscopy; intersection cohomology and $L2$-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 this volume as Picard modular surfaces. The contributors have provided a coherent and thorough account of necessary ideas and techniques, many of which are novel and not previously published.

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