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2.
Regularized periods of discrete Eisenstein series for
GL2n/GLn ✕ GLn
, (In Preparation, Slides).
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We prove a formula relating regularized periods of cuspidal Eisenstein series to cuspidal intertwining periods for
linear models. We then establish the Maass-Selberg relations for linear models. Finally, using the Maass-Selberg relations,we prove
a formula relating regularized periods of discrete Eisenstein series to discrete intertwining periods for GL2n/GLn ✕ GLn.
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We prove the motivic classes in the motivic cohomology groups of Picard modular surfaces with nontrivial coefficients constructed in [LSZ] are in the motivic cohomology groups of the
interior motives. Then we establish a relation between the motivic classes and non-critical values of the motivic L-functions associated to
cuspidal automorphic representations of GU(2,1), thus deducing non-triviality of the motivic classes and providing evidence for Beilinson's conjectures.
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