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Automorphic Forms And Shimura Varieties Of Pgsp(2)by Yuval Z Flicker
World Scientific 2005; US$ 95.00The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called ?liftings.? This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic... more...
Families of Automorphic Formsby Roelof W. Bruggeman
Springer 2009; US$ 39.95This book gives a systematic treatment of real analytic automorphic forms on the upper half plane for general confinite discrete subgroups. These automorphic forms are allowed to have exponential growth at the cusps and singularities at other points as well. It is shown that the Poincaré series and Eisenstein series occur in families of automorphic forms of this general type. These families are meromorphic in the spectral parameter and the multiplier system jointly. The general part of the book closes with a study of the singularities of these families. The work is aimed primarily at mathematicians working on real analytic automorphic forms. However, the book will also encourage readers at the graduate level (already versed in the subject and... more...
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