Smooth-automorphic Forms And Smooth-automorphic Representations (Series On Number Theory And Its Applications)

This book provides a thorough introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F. Our approach to automorphic representations is, however, different to what one usually finds in the literature: We do not restrict ourselves to considering "K-finite" automorphic forms, but allow a richer class of only smooth functions. In this way, we regain a perfect symmetry between the archimedean and the non-archimedean places of our number field F, making our bigger space of "smooth-automorphic forms" a proper, continuous representation of the full group of adelic points of G.

This book is a unique source, where a theory of "smooth-automorphic representations" is developed and presented in great detail.

Dr Harald Grobner's main scientific interests are located within the vital area of cohomological automorphic forms and their applications to number theory. He is particularly interested in the arithmetic and analytic theory of L-functions. This includes local and global representation theory and aspects in the geometry of arithmetically defined varieties.