Automorphic Forms and L-Functions for the Group GL(n,R) by Dorian Goldfeld

Automorphic Forms and L-Functions for the Group GL(n,R) Dorian Goldfeld ebook
ISBN: 9781107565029
Format: pdf
Page: 508
Publisher: Cambridge University Press

L-functions associated to automorphic forms encode all classical number theoretic information. One has the usual completion of Q as R and a. The function ζ(s) admits a meromorphic continuation to all Let χ : (Z/NZ)× → C1 := {z ∈ C : |z| = 1} be a group homomorphism. Further, not all discrete series are holomorphic, and when a group does have what is readily describable is not the automorphic form(s) but the L-functions. About Multiplicity one theorem for GL(n) by Shalika (1974, Annals of Math). Theory of admissible (g,K∞) modules for GL(2,R) 8. With finite multiplicities, by proving that the operators naturally induced by test functions on the group are compact . The classical theory of automorphic forms for GL(2) 4. Automorphic Representations and L-Functions for the General Linear Group They also include concrete examples of both global and local representations of GL(n), and present their associated L-functions. They are akin to elementary particles in physics. /number-theory/automorphic-forms-and-l-functions-group-glnr). Automorphic forms and L-functions for the group GL(n, R). AUTOMORPHIC REPRESENTATIONS OF GLn AND THEIR L FUNCTIONS, Modular Forms. Some automorphic spectral theory for GL(n,Z): [ (revision) Moments for L-functions for GL(r) x GL(r-1)] . A self-contained graduate-level introduction to the topic of L-functions, first published in 2006.