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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 class in the motivic cohomology of Picard modular surfaces with nontrivial coefficients constructed in [LSZ] is in the motivic cohomology of the
interior motive. Then we establish a relation between the motivic class and a non-critical value of the motivic L-function associated to some
cuspidal automorphic representation of GU(2,1), thus providing evidence for Beilinson's conjecture.
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