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Topic: Eisenstein series


  
  Vignettes on automorphic and modular forms, representations, L-functions, and number theory
A version of it will appear in the AIM conference volume on Eisenstein series, likely as a too-long appendix to a paper of Michael Harris', namely "A simple proof of rationality of Siegel-Weil Eisenstein series" [http://www.math.jussieu.fr/~harris/SW.pdf] which does explain something of the context.
The absolutely simplest case: spherical Eisenstein series for SL(2,Z), of course, assuming basic results from the theory of the constant term, paying attention to the proper notion of truncation.
Used in reduction of the non-maximal parabolic case to the maximal parabolic case in treatment of Eisenstein series, and in the proof (for the Selberg-Bernstein argument for meromorphic continuation) that a composition of weakly holomorphic morphisms of topological vectorspaces maps is again weakly holomorphic.
www.math.umn.edu /~garrett/m/v   (1519 words)

  
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 Daniel Bump
Gauss Sum Combinatorics and Metaplectic Eisenstein series, with Ben Brubaker and Solomon Friedberg.
Moments of the Riemann Zeta Function and Eisenstein Series II with Jennifer Beineke (in Journal of Number Theory).
Whittaker-Fourier Coefficients of Metaplectic Eisenstein Series with William Banks and Daniel Lieman.
math.stanford.edu /~bump   (725 words)

  
 ARCC Workshop: Eisenstein Series and Applications
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions.
A central goal of the workshop will be to try to understand the common structural properties of the Eisenstein series occuring in these and related applications.
For example, is it possible to identify a class of Eisenstein series whose Fourier coefficients (resp.
aimath.org /ARCC/workshops/eisenstein.html   (412 words)

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