Explicit Constructions of Automorphic L-Functions (Lecture Notes in Mathematics, 1254) 1987th Edition by Stephen Gelbart (PDF)

Description

The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This LMN is very easy to read, detailed with clear illustration and super useful. A very beautiful reference or self-taught text book for a foundation of Rankin-Selberg convolution of GxGL(n) with G classical group of rank n. Meantime, it also have a nice brief summary of Bernstein-Zelevinsky’s derivatives of smooth representations of the mirabolic subgroups.

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